AbstractIf G is a totally disconnected group and H is a closed subgroup then, according to the Gelfand–Kazhdan Lemma, if the double coset space H⧹G/H is preserved by an antiautomorphism of G of order two then (G,H) must be a Gelfand pair in the sense that HomH(π,1) has dimension at most one for each irreducible, admissible representation π of G. Under certain rather general restrictions, we show that if the symmetry property holds only for almost all double cosets, then (G,H) is a supercuspidal Gelfand pair in the sense that dimHomH(π,1) for all irreducible, supercuspidal representations π of G. There exist examples of supercuspidal Gelfand pairs which are not Gelfand pairs
A topological group G together with a compact subgroup K are said to form a Gelfand pair if the set ...
. Let K be a closed subgroup of U (n) acting on the (2n+1)-dimensional Heisenberg group Hn by automo...
Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-freene...
AbstractIf G is a totally disconnected group and H is a closed subgroup then, according to the Gelfa...
We first prove, for pairs consisting of a simply connected complex reductive group together with a c...
AbstractIn this paper, we attempt to prove that the symmetric pairs (Sp4n(F),Sp2n(E)) and (GSp4n(F),...
AbstractLetSbe a connected and simply connected unimodular solvable Lie group andKa connected compac...
We show that the $\mathcal{H}_{n-1}$-conjugacy classes of $\mathcal{H}_n,$ where $\mathcal{H}_n$ is ...
. There has been a great deal of study recently of so-called generalized Gelfand pairs; that is, cou...
Let \(G\) be a topological locally compact, Hausdorff and second countable groupoid with a Haar syst...
AbstractLet G = SO0(1,n) or SU(1,n) and K a maximal compact subgroup of G. It is proved that each ir...
AbstractWe show that the action of the group G on each level of the rooted binary tree T2 is 2-point...
AbstractWe show how to deduce multiplicity one theorems for cuspidal representations of finite group...
Let K be a compact subgroup of a real Lie group G. The homogeneous space G/K is called commutative o...
Abstract. An irreducible supercuspidal representation pi of G = GL(n, F), where F is a nonarchimed-e...
A topological group G together with a compact subgroup K are said to form a Gelfand pair if the set ...
. Let K be a closed subgroup of U (n) acting on the (2n+1)-dimensional Heisenberg group Hn by automo...
Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-freene...
AbstractIf G is a totally disconnected group and H is a closed subgroup then, according to the Gelfa...
We first prove, for pairs consisting of a simply connected complex reductive group together with a c...
AbstractIn this paper, we attempt to prove that the symmetric pairs (Sp4n(F),Sp2n(E)) and (GSp4n(F),...
AbstractLetSbe a connected and simply connected unimodular solvable Lie group andKa connected compac...
We show that the $\mathcal{H}_{n-1}$-conjugacy classes of $\mathcal{H}_n,$ where $\mathcal{H}_n$ is ...
. There has been a great deal of study recently of so-called generalized Gelfand pairs; that is, cou...
Let \(G\) be a topological locally compact, Hausdorff and second countable groupoid with a Haar syst...
AbstractLet G = SO0(1,n) or SU(1,n) and K a maximal compact subgroup of G. It is proved that each ir...
AbstractWe show that the action of the group G on each level of the rooted binary tree T2 is 2-point...
AbstractWe show how to deduce multiplicity one theorems for cuspidal representations of finite group...
Let K be a compact subgroup of a real Lie group G. The homogeneous space G/K is called commutative o...
Abstract. An irreducible supercuspidal representation pi of G = GL(n, F), where F is a nonarchimed-e...
A topological group G together with a compact subgroup K are said to form a Gelfand pair if the set ...
. Let K be a closed subgroup of U (n) acting on the (2n+1)-dimensional Heisenberg group Hn by automo...
Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-freene...