Related papers: A note on the local Weyl formula on compact Lie gr…
We compute the lower bound estimate for the module category weight of compact exceptional Lie groups by analyzing several Eilenberg--Moore type spectral sequences.
The Weyl integration model presented by An and Wang can be effectively used to reduce the integration over $G$-space. In this paper, we construct an especial Weyl integration model for KAK decomposition of Reductive Lie Group and obtain an…
Given a grading $\Gamma: A=\oplus_{g\in G}A_g$ on a nonassociative algebra $A$ by an abelian group $G$, we have two subgroups of the group of automorphisms of $A$: the automorphisms that stabilize each homogeneous component $A_g$ (as a…
The reflections in a Coxeter group are defined as conjugates of a single generator, and thus admit palindromic expressions as products of generators. Our main result gives closed formulas providing a palindromic reduced expression for each…
We generalize the Cauchy-Davenport theorem to locally compact groups.
We study the conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable (relative discrete series) unitary representations, that fit together to form a filtration by normal subgroups. Then we use that…
The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…
Let $\G$ be a locally compact group satisfying some technical requirements and $\wG$ its unitary dual. Using the theory of twisted crossed product $C^*$-algebras, we develop a twisted global quantization for symbols defined on $\G\times\wG$…
Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…
The purpose of this paper is to begin an exploration of connections between the Baum-Connes conjecture in operator $\K$-theory and the geometric representation theory of reductive Lie groups. Our initial goal is very modest, and we shall…
An expansion of the Weyl function of a $H$-selfadjoint random matrix with one negative square is provided. It is shown that the coefficients converge to a certain generalization of Catlan numbers. Properties of this generalization are…
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…
We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.
This note presents a procedure to determine the reduction of the irreducible and the induced characters of the symmetric group in terms of the irreducible and induced characters of the hyperoctahedral group Key Words: Symmetric Group,…
We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a…
A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an…
We show that a Weyl law holds for the variational spectrum of the $p$-Laplacian. More precisely, let $(\lambda_i)_{i=1}^\infty$ be the variational spectrum of $\Delta_p$ on a closed Riemannian manifold $(X,g)$ and let $N(\lambda) = \#\{i:\,…
We present a short proof of the fact that the Weyl quantisation of a tempered distribution with compactly supported Fourier transform is in the Schatten $p$-class if and only if the symbol is $L^p$-integrable. The proof is based on…
We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.
We introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study properties. Our approach is slightly different from the one introduced in the thesis of S.~Roy and, unlike the investigations…