Expand all Collapse all | Results 1 - 9 of 9 |
1. CJM 2012 (vol 66 pp. 700)
Inversion of the Radon Transform on the Free Nilpotent Lie Group of Step Two Let $F_{2n,2}$ be the free nilpotent Lie group of step two on $2n$
generators, and let $\mathbf P$ denote the affine automorphism group
of $F_{2n,2}$. In this article the theory of continuous wavelet
transform on $F_{2n,2}$ associated with $\mathbf P$ is developed,
and then a type of radial wavelets is constructed. Secondly, the
Radon transform on $F_{2n,2}$ is studied and two equivalent
characterizations of the range for Radon transform are given.
Several kinds of inversion Radon transform formulae
are established. One is obtained from the Euclidean Fourier transform, the others are from group Fourier transform. By using wavelet transform we deduce an inversion formula of the Radon
transform, which
does not require the smoothness of
functions if the wavelet satisfies the differentiability property.
Specially, if $n=1$, $F_{2,2}$ is the $3$-dimensional Heisenberg group $H^1$, the
inversion formula of the Radon transform is valid which is
associated with the sub-Laplacian on $F_{2,2}$. This result cannot
be extended to the case $n\geq 2$.
Keywords:Radon transform, wavelet transform, free nilpotent Lie group, unitary representation, inversion formula, sub-Laplacian Categories:43A85, 44A12, 52A38 |
2. CJM 2012 (vol 65 pp. 66)
On Flag Curvature of Homogeneous Randers Spaces In this paper we give an explicit formula for the flag curvature of
homogeneous Randers spaces of Douglas type and apply this formula to
obtain some interesting results. We first deduce an explicit formula
for the flag curvature of an arbitrary left invariant Randers metric
on a two-step nilpotent Lie group. Then we obtain a classification of
negatively curved homogeneous Randers spaces of Douglas type. This
results, in particular, in many examples of homogeneous non-Riemannian
Finsler spaces with negative flag curvature. Finally, we prove a
rigidity result that a homogeneous Randers space of Berwald type whose
flag curvature is everywhere nonzero must be Riemannian.
Keywords:homogeneous Randers manifolds, flag curvature, Douglas spaces, two-step nilpotent Lie groups Categories:22E46, 53C30 |
3. 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 |
4. 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 |
5. 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 |
6. CJM 2007 (vol 59 pp. 638)
Distance from Idempotents to Nilpotents We give bounds on the distance from a non-zero idempotent to the
set of nilpotents in the set of $n\times n$ matrices in terms of
the norm of the idempotent. We construct explicit idempotents and
nilpotents which achieve these distances, and determine exact
distances in some special cases.
Keywords:operator, matrix, nilpotent, idempotent, projection Categories:47A15, 47D03, 15A30 |
7. CJM 2007 (vol 59 pp. 296)
Bol Loops of Nilpotence Class Two Call a non-Moufang Bol loop \emph{minimally non-Moufang}
if every proper subloop is Moufang and
\emph{minimally nonassociative} if every proper subloop is
associative. We prove that these concepts are
the same for Bol loops which are nilpotent of
class two and in which certain associators square to $1$.
In the process, we derive many commutator and associator identities
which hold in such loops.
Keywords:Bol loop, Moufang loop, nilpotent, commutator, associator, minimally nonassociative Category:20N05 |
8. CJM 2005 (vol 57 pp. 750)
Sur la structure transverse Ã une orbite nilpotente adjointe We are interested in Poisson structures to
transverse nilpotent adjoint orbits in a complex semi-simple Lie algebra,
and we study their polynomial nature. Furthermore, in the case
of $sl_n$,
we construct some families of nilpotent orbits with quadratic
transverse structures.
Keywords:nilpotent adjoint orbits, conormal orbits, Poisson transverse structure Categories:22E, 53D |
9. CJM 1998 (vol 50 pp. 525)
Nilpotent orbit varieties and the atomic decomposition of the $q$-Kostka polynomials We study the coordinate rings~$k[\Cmubar\cap\hbox{\Frakvii t}]$ of
scheme-theoretic
intersections of nilpotent orbit closures with the diagonal matrices.
Here $\mu'$ gives the Jordan block structure of the nilpotent matrix.
de Concini and Procesi~\cite{deConcini&Procesi} proved a conjecture of
Kraft~\cite{Kraft} that these rings are isomorphic to the cohomology
rings of the varieties constructed by
Springer~\cite{Springer76,Springer78}. The famous $q$-Kostka
polynomial~$\Klmt(q)$ is the Hilbert series for the
multiplicity of the irreducible symmetric group representation indexed
by~$\lambda$ in the ring $k[\Cmubar\cap\hbox{\Frakvii t}]$.
\LS~\cite{L&S:Plaxique,Lascoux} gave combinatorially a decomposition
of~$\Klmt(q)$ as a sum of ``atomic'' polynomials with
non-negative integer coefficients, and Lascoux proposed a
corresponding decomposition in the cohomology model.
Our work provides a geometric interpretation of the atomic
decomposition. The Frobenius-splitting results of Mehta and van der
Kallen~\cite{Mehta&vanderKallen} imply a direct-sum decomposition of
the ideals of nilpotent orbit closures, arising from the inclusions of
the corresponding sets. We carry out the restriction to the diagonal
using a recent theorem of Broer~\cite{Broer}. This gives a direct-sum
decomposition of the ideals yielding the $k[\Cmubar\cap
\hbox{\Frakvii t}]$, and a new proof of the atomic decomposition of
the $q$-Kostka polynomials.
Keywords:$q$-Kostka polynomials, atomic decomposition, nilpotent conjugacy classes, nilpotent orbit varieties Categories:05E10, 14M99, 20G05, 05E15 |