Expand all Collapse all | Results 26 - 50 of 121 |
26. CJM 2011 (vol 63 pp. 327)
Discrete Series for $p$-adic $SO(2n)$ and Restrictions of Representations of $O(2n)$
In this paper we give a classification of discrete series for
$SO(2n,F)$, $F$ $p$-adic, similar to that of
MÅglin--TadiÄ for
the other classical groups. This is obtained by taking the
MÅglin--TadiÄ classification for $O(2n,F)$ and studying how the
representations restrict to $SO(2n,F)$. We then extend this to an
analysis of how admissible representations of $O(2n,F)$ restrict.
Category:22E50 |
27. CJM 2010 (vol 62 pp. 1340)
Holomorphie des opÃ©rateurs d'entrelacement normalisÃ©s Ã l'aide des paramÃ¨tres d'Arthur
In this paper we prove holomorphy for certain intertwining operators
arising from the theory of Eisenstein series. To do that we need to
normalize using the Langlands--Shahidi's normalization arising from
the twisted endoscopy and the associated representations of the
general linear group.
Categories:22E50, 22E35 |
28. CJM 2010 (vol 62 pp. 1310)
Iwahori--Hecke Algebras of $SL_2$ over $2$-Dimensional Local Fields
In this paper we construct an analogue of Iwahori--Hecke algebras of $\operatorname{SL}_2$ over $2$-dimensional local fields. After considering coset decompositions of double cosets of a Iwahori subgroup, we define a convolution product on the space of certain functions on $\operatorname{SL}_2$, and prove that the product is well-defined, obtaining a Hecke algebra. Then we investigate the structure of the Hecke algebra. We determine the center of the Hecke algebra and consider Iwahori--Matsumoto type relations.
Categories:22E50, 20G25 |
29. CJM 2010 (vol 62 pp. 914)
Reducibility of the Principal Series for Sp^{~}_{2}(F) over a p-adic Field Let $G_n=\mathrm{Sp}_n(F)$ be the rank $n$ symplectic group with
entries in a nondyadic $p$-adic field $F$. We further let $\widetilde{G}_n$ be
the metaplectic extension of $G_n$ by $\mathbb{C}^{1}=\{z\in\mathbb{C}^{\times}
\mid |z|=1\}$ defined using the Leray cocycle. In this paper, we aim to
demonstrate the complete list of reducibility points of the genuine
principal series of ${\widetilde{G}_2}$. In most cases, we will use
some techniques developed by TadiÄ that analyze the Jacquet
modules with respect to all of the parabolics containing a fixed
Borel. The exceptional cases involve representations induced from
unitary characters $\chi$ with $\chi^2=1$. Because such
representations $\pi$ are unitary, to show the irreducibility of
$\pi$, it suffices to show that
$\dim_{\mathbb{C}}\mathrm{Hom}_{{\widetilde{G}}}(\pi,\pi)=1$. We will accomplish this
by examining the poles of certain intertwining operators associated to
simple roots. Then some results of Shahidi and Ban decompose arbitrary
intertwining operators into a composition of operators corresponding
to the simple roots of ${\widetilde{G}_2}$. We will then be able to
show that all such operators have poles at principal series
representations induced from quadratic characters and therefore such
operators do not extend to operators in
$\mathrm{Hom}_{{\widetilde{G}_2}}(\pi,\pi)$ for the $\pi$ in question.
Categories:22E50, 11F70 |
30. CJM 2010 (vol 62 pp. 1116)
Degenerate p-Laplacian Operators and Hardy Type Inequalities on
H-Type Groups Let $\mathbb G$ be a step-two nilpotent group of H-type with Lie algebra $\mathfrak G=V\oplus \mathfrak t$. We define a class of vector fields $X=\{X_j\}$ on $\mathbb G$ depending on a real parameter $k\ge 1$, and we consider the corresponding $p$-Laplacian operator $L_{p,k} u= \operatorname{div}_X (|\nabla_{X} u|^{p-2} \nabla_X u)$. For $k=1$ the vector fields $X=\{X_j\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$; for $\mathbb G$ being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.
Keywords:fundamental solutions, degenerate Laplacians, Hardy inequality, H-type groups Categories:35H30, 26D10, 22E25 |
31. CJM 2010 (vol 62 pp. 563)
Whittaker Functions on Real Semisimple Lie Groups of Rank Two We give explicit formulas for Whittaker functions on real semisimple Lie groups of real rank two belonging to the class one principal series representations. By using these formulas we compute certain archimedean zeta integrals.
Categories:11F70, 22E30 |
32. CJM 2009 (vol 62 pp. 94)
The Langlands Correspondence on the Generic Irreducible Constituents of Principal Series Let $G$ be a connected semisimple split group over a $p$-adic field.
We establish the explicit link between principal nilpotent
orbits and the irreducible constituents of principal series
in terms of $L$-group objects.
Keywords:Langlands correspondence, nilpotent orbits, principal series Categories:22E50, 22E35 |
33. CJM 2009 (vol 62 pp. 52)
An Algebraic Approach to Weakly Symmetric Finsler Spaces In this paper, we introduce a new algebraic notion, weakly symmetric
Lie algebras, to give an algebraic description of an
interesting class of homogeneous Riemann--Finsler spaces, weakly symmetric
Finsler spaces. Using this new definition, we are able to give a
classification of weakly symmetric Finsler spaces with dimensions $2$
and $3$. Finally, we show that all the non-Riemannian reversible weakly
symmetric Finsler spaces we find are non-Berwaldian and with vanishing
S-curvature. This means that reversible non-Berwaldian Finsler spaces
with vanishing S-curvature may exist at large. Hence the generalized
volume comparison theorems due to Z. Shen are valid for a rather large
class of Finsler spaces.
Keywords:weakly symmetric Finsler spaces, weakly symmetric Lie algebras, Berwald spaces, S-curvature Categories:53C60, 58B20, 22E46, 22E60 |
34. CJM 2009 (vol 61 pp. 1325)
Uniqueness of Shalika Models Let $\BF_q$ be a finite field of $q$ elements, $\CF$ a $p$-adic field,
and $D$ a quaternion division algebra over $\CF$. This paper proves
uniqueness of Shalika models for $\GL_{2n}(\BF_q) $ and $\GL_{2n}(D)$,
and re-obtains uniqueness of Shalika models for $\GL_{2n}(\CF)$ for
any $n\in \BN$.
Keywords:Shalika models, linear models, uniqueness, multiplicity free Category:22E50 |
35. CJM 2009 (vol 61 pp. 1407)
Traces, Cross-Ratios and 2-Generator Subgroups of $\SU(2,1)$ In this work, we investigate how to decompose a pair $(A,B)$ of
loxodromic isometries of the complex hyperbolic plane $\mathbf H^{2}_{\mathbb C}$ under
the form $A=I_1I_2$ and $B=I_3I_2$, where the $I_k$'s are
involutions. The main result is a decomposability criterion, which
is expressed in terms of traces of elements of the group $\langle
A,B\rangle$.
Categories:14L24, 22E40, 32M15, 51M10 |
36. CJM 2009 (vol 61 pp. 1375)
Stable Discrete Series Characters at Singular Elements Write $\Theta^E$ for the stable discrete series character associated
with an irreducible finite-dimensional representation $E$ of a connected
real reductive group $G$. Let $M$ be the centralizer of the split
component of a maximal torus $T$, and denote by $\Phi_M(\gm,\Theta^E)$
Arthur's extension of $ |D_M^G(\gm)|^{\lfrac 12}
\Theta^E(\gm)$ to $T(\R)$. In this paper we give a simple
explicit expression for
$\Phi_M(\gm,\Theta^E)$ when $\gm$ is elliptic in $G$. We do not assume $\gm$ is regular.
Category:22E47 |
37. CJM 2009 (vol 61 pp. 961)
Transfert des intÃ©grales orbitales pour les algÃ¨bres de Lie classiques Dans cet article, on consid\`ere un groupe semi-simple $\rmG$ classique
r\'eel et connexe. On suppose de plus que $\rmG$ poss\`ede un
sous-groupe de Cartan compact. On d\'efinit une famille de
sous-alg\`ebres de Lie associ\'ee \`a $\g = \Lie(\rmG)$, de m\^eme rang
que $\g$ dont tous les facteurs simples sont de rang $1$ ou~$2$.
Soit $\g'$ une telle sous-alg\`ebre de Lie. On construit alors une
application de transfert des int\'egrales orbitales de $\g'$ dans
l'espace des int\'egrales orbitales de $\g$. On montre que cette
application est d\'efinie d\`es que $\g$ ne poss\`ede pas de facteur
simple r\'eel de type $\CI$ de rang sup\'erieur ou \'egal \`a $3$.
Si de plus, $\g$ ne poss\`ede pas de facteur simple de type $\BI$ de
rang sup\'erieur \`a $3$, on montre la surjectivit\'e de cette
application de transfert.
On utilise cette application de transfert pour obtenir une formule de
r\'eduction de l'int\'egrale de Cauchy Harish-Chandra pour les paires
duales d'alg\`ebres de Lie r\'eductives $\bigl( \Ug(p,q),\Ug(r,s)
\bigr)$ et $\bigl( \Sp(p,q),\Og^*(2n) \bigr)$ avec $p+q = r+s = n$.
Categories:22E30, 22E46 |
38. CJM 2009 (vol 61 pp. 779)
Residual Spectra of Split Classical Groups and their Inner Forms This paper is concerned with the residual spectrum of the
hermitian quaternionic classical groups $G_n'$ and $H_n'$ defined
as algebraic groups for a quaternion algebra over an algebraic
number field. Groups $G_n'$ and
$H_n'$ are not quasi-split. They are inner forms of the split
groups $\SO_{4n}$ and $\Sp_{4n}$. Hence, the parts of the residual
spectrum of $G_n'$ and $H_n'$ obtained in this paper are compared
to the corresponding parts for the split groups $\SO_{4n}$ and
$\Sp_{4n}$.
Categories:11F70, 22E55 |
39. CJM 2009 (vol 61 pp. 708)
Regular Homeomorphisms of Finite Order on Countable Spaces We present a structure theorem for a broad class of homeomorphisms of
finite order on countable zero dimensional spaces. As applications we
show the following.
\begin{compactenum}[\rm(a)]
\item Every countable nondiscrete topological group not containing an
open Boolean subgroup can be partitioned into infinitely many dense
subsets.
\item If $G$ is a countably infinite Abelian group with finitely many
elements of order $2$ and $\beta G$ is the Stone--\v Cech
compactification of $G$ as a discrete semigroup, then for every
idempotent $p\in\beta G\setminus\{0\}$, the subset
$\{p,-p\}\subset\beta G$ generates algebraically the free product of
one-element semigroups $\{p\}$ and~$\{-p\}$.
\end{compactenum}
Keywords:Homeomorphism, homogeneous space, topological group, resolvability, Stone-\v Cech compactification Categories:22A30, 54H11, 20M15, 54A05 |
40. CJM 2009 (vol 61 pp. 691)
Prehomogeneity on Quasi-Split Classical Groups and Poles of Intertwining Operators Suppose that $P=MN$ is a maximal parabolic subgroup of a quasisplit,
connected, reductive classical group $G$ defined over a non-Archimedean
field and $A$ is the standard intertwining operator attached to a
tempered representation of $G$ induced from $M$. In this paper we
determine all the cases in which $\Lie(N)$ is
prehomogeneous under $\Ad(m)$ when $N$ is non-abelian, and give necessary
and sufficient conditions for $A$ to have a pole at $0$.
Categories:22E50, 20G05 |
41. CJM 2009 (vol 61 pp. 373)
An Infinite Order Whittaker Function In this paper we construct a flat smooth section of an induced space
$I(s,\eta)$ of $SL_2(\mathbb{R})$ so that the attached Whittaker function
is not of finite order.
An asymptotic method of classical analysis is used.
Categories:11F70, 22E45, 41A60, 11M99, 30D15, 33C15 |
42. CJM 2009 (vol 61 pp. 427)
On Reducibility and Unitarizability for Classical $p$-Adic Groups, Some General Results The aim of this paper is to prove two general results on parabolic
induction of classical $p$-adic groups (actually, one of them holds also
in the archimedean case), and to obtain from them some consequences about
irreducible unitarizable representations. One of these consequences is a
reduction of the unitarizability problem for these groups. This
reduction is similar to the reduction of the unitarizability problem
to the case of real infinitesimal
character for real reductive groups.
Categories:22E50, 22E35 |
43. CJM 2009 (vol 61 pp. 351)
Multiplication of Polynomials on Hermitian Symmetric spaces and Littlewood--Richardson Coefficients Let $K$ be a complex reductive algebraic group and $V$ a
representation of $K$. Let $S$ denote the ring of polynomials on
$V$. Assume that the action of $K$ on $S$ is multiplicity-free. If
$\lambda$ denotes the isomorphism class of an irreducible
representation of $K$, let $\rho_\lambda\from K \rightarrow
GL(V_{\lambda})$ denote the corresponding irreducible representation
and $S_\lambda$ the $\lambda$-isotypic component of $S$. Write
$S_\lambda \cdot S_\mu$ for the subspace of $S$ spanned by products of
$S_\lambda$ and $S_\mu$. If $V_\nu$ occurs as an irreducible
constituent of $V_\lambda\otimes V_\mu$, is it true that
$S_\nu\subseteq S_\lambda\cdot S_\mu$? In this paper, the authors
investigate this question for representations arising in the context
of Hermitian symmetric pairs. It is shown that the answer is yes in
some cases and, using an earlier result of Ruitenburg, that in the
remaining classical cases, the answer is yes provided that a
conjecture of Stanley on the multiplication of Jack polynomials is
true. It is also shown how the conjecture connects multiplication in
the ring $S$ to the usual Littlewood--Richardson rule.
Keywords:Hermitian symmetric spaces, multiplicity free actions, Littlewood--Richardson coefficients, Jack polynomials Categories:14L30, 22E46 |
44. CJM 2009 (vol 61 pp. 222)
Klyachko Models for General Linear Groups of Rank 5 over a $p$-Adic Field This paper shows the existence and uniqueness of Klyachko models for
irreducible unitary representations of $\GL_5(\CF)$, where $\CF$ is
a $p$-adic field. It is an extension of the work of Heumos and Rallis on $\GL_4(\CF)$.
Keywords:Klyachko models, Whittaker-symplectic model Category:22E50 |
45. CJM 2008 (vol 60 pp. 1306)
Theta Lifts of Tempered Representations for Dual Pairs $(\Sp_{2n}, O(V))$ This paper is the continuation of our previous work on the explicit
determination of the structure of theta lifts for dual pairs
$(\Sp_{2n}, O(V))$ over a non-archimedean field $F$ of characteristic
different than $2$, where $n$ is the split rank of $\Sp_{2n}$ and the
dimension of the space $V$ (over $F$) is even. We determine the
structure of theta lifts of tempered representations in terms of theta
lifts of representations in discrete series.
Categories:22E35, 22E50, 11F70 |
46. CJM 2008 (vol 60 pp. 1001)
Isometric Group Actions on Hilbert Spaces: Structure of Orbits Our main result is that a finitely generated nilpotent group has
no isometric action on an infinite-dimensional Hilbert space with
dense orbits. In contrast, we construct such an action with a
finitely generated metabelian group.
Keywords:affine actions, Hilbert spaces, minimal actions, nilpotent groups Categories:22D10, 43A35, 20F69 |
47. CJM 2008 (vol 60 pp. 1067)
On Types for Unramified $p$-Adic Unitary Groups Let $F$ be a non-archimedean local field of residue characteristic
neither 2 nor 3 equipped with a galois involution with fixed field
$F_0$, and let $G$ be a symplectic group over $F$ or an unramified
unitary group over $F_0$. Following the methods of Bushnell--Kutzko for
$\GL(N,F)$, we define an analogue of a simple type attached to a
certain skew simple stratum, and realize a type in $G$. In
particular, we obtain an irreducible supercuspidal representation of
$G$ like $\GL(N,F)$.
Keywords:$p$-adic unitary group, type, supercuspidal representation, Hecke algebra Categories:22E50, 22D99 |
48. CJM 2008 (vol 60 pp. 790)
Types, paquets et changement de base : l'exemple de $U(2,1)(F_0)$. I. Types simples maximaux et paquets singletons |
Types, paquets et changement de base : l'exemple de $U(2,1)(F_0)$. I. Types simples maximaux et paquets singletons Soit $F_0$ un corps local non archim\'edien de caract\'eristique
nulle et de ca\-rac\-t\'eristique r\'esiduelle impaire.
J. Rogawski a montr\'e l'existence du changement de base entre le
groupe unitaire en trois variables $U(2,1)(F_{0})$, d\'efini
relativement \`a une extension quadratique $F$ de $F_{0}$, et le
groupe lin\'eaire $GL(3,F)$. Par ailleurs, nous
avons d\'ecrit les repr\'esentations supercuspidales irr\'eductibles
de $U(2,1)(F_{0})$ comme induites \`a partir d'un sous-groupe compact
ouvert de $U(2,1)(F_{0})$, description analogue \`a celle des
repr\'esentations admissibles irr\'eductibles de $GL(3,F)$ obtenue
par C. Bushnell et P. Kutzko. A partir de ces
descriptions, nous construisons explicitement le changement de base
des repr\'esentations tr\`es cuspidales de $U(2,1)(F_{0})$.
Categories:22E50, 11F70 |
49. CJM 2008 (vol 60 pp. 412)
Quelques calculs de traces compactes et leurs transform{Ã©es de Satake On calcule les restrictions {\`a} l'alg{\`e}bre de Hecke sph{\'e}rique
des traces tordues compactes d'un ensemble de repr{\'e}sentations
explicitement construites du groupe $\GL(N, F)$, o{\`u} $F$ est
un corps $p$-adique. Ces calculs r\'esolve en particulier une
question pos{\'e}e dans un article pr\'ec\'edent du m\^eme auteur.
Categories:22E50, 11F70 |
50. CJM 2007 (vol 59 pp. 1301)
Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group We prove dispersive and Strichartz inequalities for the solution of the wave
equation related to the full
Laplacian on the Heisenberg group, by means of Besov spaces defined by a
Littlewood--Paley
decomposition related to the spectral resolution of the full Laplacian.
This requires a careful
analysis due also to the non-homogeneous nature of the full Laplacian.
This result has to be compared to a previous one by Bahouri, G\'erard
and Xu concerning the solution of the wave equation related to
the Kohn Laplacian.
Keywords:nilpotent and solvable Lie groups, smoothness and regularity of solutions of PDEs Categories:22E25, 35B65 |