Expand all Collapse all | Results 1 - 25 of 359 |
1. CJM Online first
Overconvergent Families of Siegel-Hilbert Modular Forms We construct one-parameter families of overconvergent Siegel-Hilbert
modular forms. This result has applications to construction of
Galois representations for automorphic forms of non-cohomological
weights.
Keywords:p-adic automorphic form, rigid analytic geometry Categories:11F46, 14G22 |
2. CJM Online first
Lifting Representations of Finite Reductive Groups I: Semisimple Conjugacy Classes Suppose that $\tilde{G}$ is a connected reductive group
defined over a field $k$, and
$\Gamma$ is a finite group acting via $k$-automorphisms
of $\tilde{G}$ satisfying a certain quasi-semisimplicity condition.
Then the identity component of the group of $\Gamma$-fixed points
in $\tilde{G}$ is reductive.
We axiomatize the main features of the relationship between this
fixed-point group and the pair $(\tilde{G},\Gamma)$,
and consider any group $G$ satisfying the axioms.
If both $\tilde{G}$ and $G$ are $k$-quasisplit, then we
can consider their duals $\tilde{G}^*$ and $G^*$.
We show the existence of and give an explicit formula for a natural
map from the set of semisimple stable conjugacy classes in $G^*(k)$
to the analogous set for $\tilde{G}^*(k)$.
If $k$ is finite, then our groups are automatically quasisplit,
and our result specializes to give a map
of semisimple conjugacy classes.
Since such classes parametrize packets of irreducible representations
of $G(k)$ and $\tilde{G}(k)$, one obtains a mapping of such packets.
Keywords:reductive group, lifting, conjugacy class, representation, Lusztig series Categories:20G15, 20G40, 20C33, 22E35 |
3. CJM Online first
Global holomorphic functions in several noncommuting variables We define a free holomorphic function to be a function
that is locally, with respect to the free topology, a bounded
nc-function.
We prove that free holomorphic functions are the functions that
are locally uniformly approximable
by free polynomials. We prove a realization formula and an Oka-Weil
theorem for free analytic functions.
Keywords:noncommutative analysis, free holomorphic functions Category:15A54 |
4. CJM Online first
Faithfulness of Actions on Riemann-Roch Spaces Given a faithful action of a finite group $G$ on an algebraic
curve~$X$ of genus $g_X\geq 2$, we give explicit criteria for
the induced action of~$G$ on the Riemann-Roch space~$H^0(X,\mathcal{O}_X(D))$
to be faithful, where $D$ is a $G$-invariant divisor on $X$ of
degree at least~$2g_X-2$. This leads to a concise answer to the
question when the action of~$G$ on the space~$H^0(X, \Omega_X^{\otimes
m})$ of global holomorphic polydifferentials of order $m$ is
faithful. If $X$ is hyperelliptic, we furthermore provide an
explicit basis of~$H^0(X, \Omega_X^{\otimes m})$. Finally, we
give applications in deformation theory and in coding theory
and we discuss the analogous problem for the action of~$G$ on
the first homology $H_1(X, \mathbb{Z}/m\mathbb{Z})$ if $X$ is a Riemann surface.
Keywords:faithful action, Riemann-Roch space, polydifferential, hyperelliptic curve, equivariant deformation theory, Goppa code, homology Categories:14H30, 30F30, 14L30, 14D15, 11R32 |
5. CJM Online first
Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor We study bounded derived categories of the category of representations of infinite quivers over a ring $R$. In case $R$ is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left, resp. right, rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.
Keywords:derived category, Grothendieck duality, representation of quivers, reflection functor Categories:18E30, 16G20, 18E40, 16D90, 18A40 |
6. CJM Online first
Expression d'un facteur epsilon de paire par une formule intÃ©grale Let $E/F$ be a quadratic extension of $p$-adic fields and
let $d$, $m$ be nonnegative integers of distinct parities. Fix
admissible irreducible tempered representations $\pi$ and $\sigma$ of
$GL_d(E)$ and $GL_m(E)$ respectively. We assume that $\pi$ and
$\sigma$ are conjugate-dual. That is to say $\pi\simeq \pi^{\vee,c}$
and $\sigma\simeq \sigma^{\vee,c}$ where $c$ is the non trivial
$F$-automorphism of $E$. This implies, we can extend $\pi$ to an
unitary representation $\tilde{\pi}$ of a nonconnected group
$GL_d(E)\rtimes \{1,\theta\}$. Define $\tilde{\sigma}$ the same
way. We state and prove an integral formula for
$\epsilon(1/2,\pi\times \sigma,\psi_E)$ involving the characters of
$\tilde{\pi}$ and $\tilde{\sigma}$. This formula is related to the
local Gan-Gross-Prasad conjecture for unitary groups.
Keywords:epsilon factor, twisted groups Categories:22E50, 11F85 |
7. CJM Online first
A Finite-time Condition for Exponential Trichotomy in Infinite Dynamical Systems In this article we study exponential trichotomy for infinite dimensional
discrete time dynamical systems. The goal of this article is to prove that
finite time exponential trichotomy conditions allow to derive exponential
trichotomy for any times. We present an application to the case of pseudo
orbits in some neighborhood of a normally hyperbolic set.
Keywords:exponential trichotomy, exponential dichotomy, discrete time dynamical systems, difference equations Categories:34D09, 34A10 |
8. CJM Online first
On a sumset conjecture of ErdÅs ErdÅs conjectured that for any set $A\subseteq \mathbb{N}$
with positive
lower asymptotic density, there are infinite sets $B,C\subseteq
\mathbb{N}$
such that $B+C\subseteq A$. We verify ErdÅs' conjecture in
the case that $A$ has Banach density exceeding $\frac{1}{2}$.
As a consequence, we prove that, for $A\subseteq \mathbb{N}$
with
positive Banach density (a much weaker assumption than positive
lower density), we can find infinite $B,C\subseteq \mathbb{N}$
such
that $B+C$ is contained in the union of $A$ and a translate of
$A$. Both of the aforementioned
results are generalized to arbitrary countable
amenable groups. We also provide a positive solution to ErdÅs'
conjecture for subsets of the natural numbers that are pseudorandom.
Keywords:sumsets of integers, asymptotic density, amenable groups, nonstandard analysis Categories:11B05, 11B13, 11P70, 28D15, 37A45 |
9. CJM Online first
All Irrational Extended Rotation Algebras are AF Algebras Let $\theta\in[0, 1]$ be any irrational number. It is shown that the
extended rotation algebra $\mathcal B_\theta$ introduced in
a previous paper is always an AF algebra.
Keywords:irrational rotation algebra, extended irrational rotation algebra, AF-embedding |
10. CJM Online first
A Free Product Formula for the Sofic Dimension It is proved that if $G=G_1*_{G_3}G_2$ is free product of probability
measure preserving $s$-regular ergodic discrete groupoids amalgamated
over an amenable subgroupoid $G_3$, then the sofic dimension $s(G)$
satisfies the equality
\[
s(G)=\mathfrak{h}(G_1^0)s(G_1)+\mathfrak{h}(G_2^0)s(G_2)-\mathfrak{h}(G_3^0)s(G_3)
\]
where $\mathfrak{h}$ is the normalized Haar measure on $G$.
Keywords:sofic groups, dynamical systems, orbit equivalence, free entropy Category:20E06 |
11. CJM Online first
Mahler Measures as Linear Combinations of $L$-values of Multiple Modular Forms We study the Mahler measures of certain families of Laurent
polynomials in two and three variables. Each of the known Mahler
measure formulas for these families involves $L$-values of at most one
newform and/or at most one quadratic character. In this paper, we
show, either rigorously or numerically, that the Mahler measures of
some polynomials are related to $L$-values of multiple newforms and
quadratic characters simultaneously. The results suggest that the
number of modular $L$-values appearing in the formulas significantly
depends on the shape of the algebraic value of the parameter chosen
for each polynomial. As a consequence, we also obtain new formulas
relating special values of hypergeometric series evaluated at
algebraic numbers to special values of $L$-functions.
Keywords:Mahler measures, Eisenstein-Kronecker series, $L$-functions, hypergeometric series Categories:11F67, 33C20 |
12. CJM Online first
On Varieties of Lie Algebras of Maximal Class We study complex projective varieties that parametrize
(finite-dimensional) filiform Lie algebras over ${\mathbb C}$,
using equations derived by Millionshchikov. In the
infinite-dimensional case we concentrate our attention on
${\mathbb N}$-graded Lie algebras of maximal class. As shown by A.
Fialowski
there are only
three isomorphism types of $\mathbb{N}$-graded Lie algebras
$L=\oplus^{\infty}_{i=1} L_i$ of maximal class generated by $L_1$
and $L_2$, $L=\langle L_1, L_2 \rangle$. Vergne described the
structure of these algebras with the property $L=\langle L_1
\rangle$. In this paper we study those generated by the first and
$q$-th components where $q\gt 2$, $L=\langle L_1, L_q \rangle$. Under
some technical condition, there can only be one isomorphism type
of such algebras. For $q=3$ we fully classify them. This gives a
partial answer to a question posed by Millionshchikov.
Keywords:filiform Lie algebras, graded Lie algebras, projective varieties, topology, classification Categories:17B70, 14F45 |
13. CJM Online first
Moduli Spaces of Vector Bundles over a Real Curve: $\mathbb Z/2$-Betti Numbers Moduli spaces of real bundles over a real curve arise naturally
as Lagrangian submanifolds of the moduli space of semi-stable
bundles over a complex curve. In this paper, we adapt the methods
of Atiyah-Bott's ``Yang-Mills over a Riemann Surface'' to compute
$\mathbb Z/2$-Betti numbers of these spaces.
Keywords:cohomology of moduli spaces, holomorphic vector bundles Categories:32L05, 14P25 |
14. CJM Online first
Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory We provide some new local obstructions to
approximating
tropical curves in
smooth tropical surfaces. These obstructions are based on
a
relation between tropical and complex intersection theories which is
also established here. We give
two applications of the methods developed in this paper.
First we classify all locally irreducible approximable 3-valent fan tropical
curves in a
fan tropical plane.
Secondly, we prove that a generic non-singular
tropical surface
in tropical projective 3-space contains finitely
many approximable tropical lines
if
it is of degree 3, and contains no approximable tropical lines if
it is of degree 4 or more.
Keywords:tropical geometry, amoebas, approximation of tropical varieties, intersection theory Categories:14T05, 14M25 |
15. CJM Online first
Geometric Spectra and Commensurability The work of Reid, Chinburg-Hamilton-Long-Reid,
Prasad-Rapinchuk, and the author with Reid have demonstrated that
geodesics or totally geodesic submanifolds can sometimes be used to
determine the commensurability class of an arithmetic manifold. The
main results of this article show that generalizations of these
results to other arithmetic manifolds will require a wide range of
data. Specifically, we prove that certain incommensurable arithmetic
manifolds arising from the semisimple Lie groups of the form
$(\operatorname{SL}(d,\mathbf{R}))^r \times
(\operatorname{SL}(d,\mathbf{C}))^s$ have the same commensurability
classes of totally geodesic submanifolds coming from a fixed
field. This construction is algebraic and shows the failure of
determining, in general, a central simple algebra from subalgebras
over a fixed field. This, in turn, can be viewed in terms of forms of
$\operatorname{SL}_d$ and the failure of determining the form via certain classes of
algebraic subgroups.
Keywords:arithmetic groups, Brauer groups, arithmetic equivalence, locally symmetric manifolds Category:20G25 |
16. CJM Online first
Sharp Localized Inequalities for Fourier Multipliers In the paper we study sharp localized $L^q\colon L^p$ estimates for
Fourier multipliers resulting from modulation of the jumps of
LÃ©vy
processes.
The proofs of these estimates rest on probabilistic methods and
exploit related sharp bounds for differentially subordinated
martingales, which are of independent interest. The lower bounds
for
the constants involve the analysis of laminates, a family of
certain
special probability measures on $2\times 2$ matrices. As an
application, we obtain new sharp bounds for the real and imaginary
parts of the Beurling-Ahlfors operator .
Keywords:Fourier multiplier, martingale, laminate Categories:42B15, 60G44, 42B20 |
17. CJM Online first
Values of Twisted Tensor $L$-functions of Automorphic Forms Over Imaginary Fields Let $K$ be a complex quadratic extension of $\mathbb{Q}$ and let $\mathbb{A}_K$
denote the adeles of $K$.
We find special values at all of the critical points of twisted
tensor $L$-functions attached to cohomological cuspforms on $GL_2(\mathbb{A}_K)$,
and establish Galois equivariance of the values.
To investigate the values, we determine the archimedean factors
of a class of integral representations of these $L$-functions,
thus proving a conjecture due to Ghate. We also investigate
analytic properties of these $L$-functions, such as their functional
equations.
Keywords:twisted tensor $L$-function, cuspform, hypergeometric series Categories:11F67, 11F37 |
18. CJM Online first
Toric Degenerations, Tropical Curve, and Gromov-Witten Invariants of Fano Manifolds In this paper, we give a tropical method for computing Gromov-Witten
type invariants
of Fano manifolds of special type.
This method applies to those Fano manifolds which admit toric
degenerations
to toric Fano varieties with singularities allowing small resolutions.
Examples include (generalized) flag manifolds of type A, and
some moduli space
of rank two bundles on a genus two curve.
Keywords:Fano varieties, Gromov-Witten invariants, tropical curves Category:14J45 |
19. CJM Online first
A Skolem-Mahler-Lech Theorem for Iterated Automorphisms of $K$-algebras This paper proves a commutative algebraic extension
of a generalized Skolem-Mahler-Lech theorem due to the first
author.
Let $A$ be a finitely generated commutative $K$-algebra
over a field of characteristic $0$, and let $\sigma$ be
a $K$-algebra automorphism of $A$.
Given ideals $I$ and $J$ of $A$, we show that
the set $S$ of integers $m$ such that
$\sigma^m(I) \supseteq J$ is a finite union of
complete doubly infinite arithmetic progressions in $m$, up to
the addition of a finite set.
Alternatively, this result states that for an affine scheme
$X$ of finite type over $K$,
an automorphism $\sigma \in \operatorname{Aut}_K(X)$, and $Y$ and $Z$
any two closed subschemes of $X$, the set
of integers $m$ with $\sigma^m(Z ) \subseteq Y$ is as above.
The paper presents examples
showing that this result may fail to hold if the affine scheme
$X$ is
not of finite type, or if $X$ is of finite type but the field
$K$ has positive characteristic.
Keywords:automorphisms, endomorphisms, affine space, commutative algebras, Skolem-Mahler-Lech theorem Categories:11D45, 14R10, 11Y55, 11D88 |
20. CJM 2013 (vol 66 pp. 429)
Perturbation and Solvability of Initial $L^p$ Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains |
Perturbation and Solvability of Initial $L^p$ Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains For parabolic linear operators $L$ of second order in divergence form,
we prove that the solvability of initial $L^p$ Dirichlet problems for
the whole range $1\lt p\lt \infty$ is preserved under appropriate small
perturbations of the coefficients of the operators involved.
We also prove that if the coefficients of $L$ satisfy a suitable
controlled oscillation in the form of Carleson measure conditions,
then for certain values of $p\gt 1$, the initial $L^p$ Dirichlet problem
associated to $Lu=0$ over non-cylindrical domains is solvable.
The results are adequate adaptations of the corresponding results for
elliptic equations.
Keywords:initial $L^p$ Dirichlet problem, second order parabolic equations in divergence form, non-cylindrical domains, reverse HÃ¶lder inequalities Category:35K20 |
21. CJM Online first
Symplectic Degenerate Flag Varieties A simple finite dimensional module $V_\lambda$ of a simple complex
algebraic group $G$ is naturally endowed with a filtration induced by the PBW-filtration
of $U(\mathrm{Lie}\, G)$. The associated graded space $V_\lambda^a$ is a module
for the group $G^a$, which can be roughly described as a semi-direct product of a
Borel subgroup of $G$ and a large commutative unipotent group $\mathbb{G}_a^M$. In analogy
to the flag variety $\mathcal{F}_\lambda=G.[v_\lambda]\subset \mathbb{P}(V_\lambda)$,
we call the closure
$\overline{G^a.[v_\lambda]}\subset \mathbb{P}(V_\lambda^a)$
of the $G^a$-orbit through the highest weight line the degenerate flag variety $\mathcal{F}^a_\lambda$.
In general this is a
singular variety, but we conjecture that it has many nice properties similar to
that of Schubert varieties. In this paper we consider the case of $G$ being the symplectic group.
The symplectic case is important for the conjecture
because it is the first known case where even for fundamental weights $\omega$ the varieties
$\mathcal{F}^a_\omega$ differ from $\mathcal{F}_\omega$. We give an explicit
construction of the varieties $Sp\mathcal{F}^a_\lambda$ and construct desingularizations,
similar to the Bott-Samelson resolutions in the classical case. We prove that $Sp\mathcal{F}^a_\lambda$
are normal locally complete intersections with terminal and rational singularities.
We also show that these varieties are Frobenius split. Using the above mentioned results, we
prove an analogue of the Borel-Weil theorem and obtain a $q$-character formula
for the characters of irreducible $Sp_{2n}$-modules via the Atiyah-Bott-Lefschetz fixed
points formula.
Keywords:Lie algebras, flag varieties, symplectic groups, representations Categories:14M15, 22E46 |
22. CJM Online first
On the Local Convexity of Intersection Bodies of Revolution One of the fundamental results in Convex Geometry is Busemann's
theorem, which states that the intersection body of a symmetric convex
body is convex. Thus, it is only natural to ask if there is a
quantitative version of Busemann's theorem, i.e., if the intersection
body operation actually improves convexity. In this paper we
concentrate on the symmetric bodies of revolution to provide several
results on the (strict) improvement of convexity under the
intersection body operation. It is shown that the intersection body of
a symmetric convex body of revolution has the same asymptotic behavior
near the equator as the Euclidean
ball. We apply this result to show that in sufficiently high
dimension the double intersection body of a symmetric convex body of
revolution is very close to an ellipsoid in the Banach-Mazur
distance. We also prove results on the local convexity at the equator
of intersection bodies in the class of star bodies of revolution.
Keywords:convex bodies, intersection bodies of star bodies, Busemann's theorem, local convexity Categories:52A20, 52A38, 44A12 |
23. CJM Online first
Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$ We obtain results on the unitary equivalence of weak contractions of
class $C_0$ to their Jordan models under an assumption on their
commutants. In particular, our work addresses the case of arbitrary
finite multiplicity. The main tool is the
theory of boundary representations due to Arveson. We also
generalize and improve previously known results concerning unitary
equivalence and similarity to Jordan models when the minimal function
is a Blaschke product.
Keywords:weak contractions, operators of class $C_0$, Jordan model, unitary equivalence Categories:47A45, 47L55 |
24. CJM Online first
Types et contragrÃ©dientes Soit $\mathrm{G}$ un groupe rÃ©ductif $p$-adique, et soit $\mathrm{R}$
un corps algÃ©briquement clos.
Soit $\pi$ une reprÃ©sentation lisse de $\mathrm{G}$ dans un espace
vectoriel $\mathrm{V}$ sur
$\mathrm{R}$.
Fixons un sous-groupe ouvert et compact $\mathrm{K}$ de $\mathrm{G}$ et une reprÃ©sentation
lisse irrÃ©ductible $\tau$ de $\mathrm{K}$ dans un espace vectoriel
$\mathrm{W}$ de dimension
finie sur $\mathrm{R}$.
Sur l'espace $\mathrm{Hom}_{\mathrm{K}(\mathrm{W},\mathrm{V})}$ agit l'algÃ¨bre
d'entrelacement $\mathscr{H}(\mathrm{G},\mathrm{K},\mathrm{W})$.
Nous examinons la compatibilitÃ© de ces constructions avec le passage aux
reprÃ©sentations contragrÃ©dientes $\mathrm{V}^Äe$ et $\mathrm{W}^Äe$, et donnons en
particulier des conditions sur $\mathrm{W}$ ou sur la caractÃ©ristique
de $\mathrm{R}$ pour que
le comportement soit semblable au cas des reprÃ©sentations complexes.
Nous prenons un point de vue abstrait, n'utilisant que des propriÃ©tÃ©s
gÃ©nÃ©rales de $\mathrm{G}$.
Nous terminons par une application Ã la thÃ©orie des types pour le groupe
$\mathrm{GL}_n$ et ses formes intÃ©rieures sur un corps local non archimÃ©dien.
Keywords:modular representations of p-adic reductive groups, types, contragredient, intertwining Category:22E50 |
25. CJM 2013 (vol 66 pp. 141)
Existence of Taut Foliations on Seifert Fibered Homology $3$-spheres This paper concerns the problem of existence of taut foliations among $3$-manifolds.
Since the contribution of David Gabai,
we know that closed $3$-manifolds with non-trivial second homology group
admit a taut foliation.
The essential part of this paper focuses on Seifert fibered homology $3$-spheres.
The result is quite different if they are integral or rational but non-integral homology $3$-spheres.
Concerning integral homology $3$-spheres, we can see that all but the $3$-sphere and the PoincarÃ© $3$-sphere admit a taut foliation.
Concerning non-integral homology $3$-spheres,
we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation.
Moreover, we show that the geometries do not determine the existence of taut foliations
on non-integral Seifert fibered homology $3$-spheres.
Keywords:homology 3-spheres, taut foliation, Seifert-fibered 3-manifolds Categories:57M25, 57M50, 57N10, 57M15 |