Related papers: Extensions of tempered representations

In this paper, we study the representations of the Hopf-Ore extensions $kG(\chi^{-1}, a, 0)$ of group algebra $kG$, where $k$ is an algebraically closed field. We classify all finite dimensional simple $kG(\chi^{-1}, a, 0)$-modules under…

A key tool for the study of an affine Hecke algebra $\mathcal{H}$ is provided by Springer theory of the Langlands dual group via the realization of $\mathcal{H}$ as equivariant $K$-theory of the Steinberg variety. We prove a similar…

Let $G$ be a complex reductive group and $H=G^{\theta}$ be its fixed point subgroup under a Galois involution $\theta$. We show that any $H$-distinguished representation $\pi$ (i.e $\mathrm{dim}_{\mathbb{C}}\left(\pi^{*}\right)^{H}\neq0$)…

Let G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here…

The simplices and the complexes arsing form the grading of the fundamental (desymmetrized) domain of arithmetical groups and non-arithmetical groups, as well as their extended (symmetrized) ones are described also for oriented manifolds in…

C. Jantzen has defined a correspondence which attaches to an irreducible representation of a classical $p$-adic group, a finite set of irreducible representations of classical $p$-adic groups supported in a single or in two cuspidal lines…

We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an…

We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…

Let $G_1,G_2$ be real reductive groups and $(\pi,V)$ a smooth, irreducible, admissible representation of $G_1 \times G_2$. We prove that $(\pi,V)$ is the completed tensor product of $(\pi_i,V_i)$, $i=1,2$, where $(\pi_i,V_i)$ is a…

Given a finite group $G$ and a subgroup $K$, we study the commutant of $\text{Ind}_K^G\theta$, where $\theta$ is an irreducible $K$-representation. After a careful analysis of Frobenius reciprocity, we are able to introduce an orthogonal…

We introduce a new class of exponentials of Artin-Hasse type, called $\boldsymbol{\pi}$-exponentials. These exponentials depends on the choice of a generator $\boldsymbol{\pi}$ of the Tate module of a Lubin-Tate group $\mathfrak{G}$ over…

In recent, H. Sun defined a new kind of refined Eulerian polynomials, namely, \begin{eqnarray*} A_n(p,q)=\sum_{\pi\in \mathfrak{S}_n}p^{{\rm odes}(\pi)}q^{{\rm edes}(\pi)} \end{eqnarray*} for $n\geq 1$, where ${odes}(\pi)$ and ${edes}(\pi)$…

The Alesker-Bernig-Schuster theorem asserts that each irreducible representation of the special orthogonal group appears with multiplicity at most one as a subrepresentation of the space of continuous translation-invariant valuations with…

This paper describes irreducible representations in category O of the rational Cherednik algebra H_c(H_3,h) associated to the exceptional Coxeter group H_3 and any complex parameter c. We compute the characters of all these representations…

Let $\mathbf{G}$ be a split algebrac group of type $E_n$ defined over a $p$-adic field. This group contains a dual pair $G \times G'$ where one of the groups is of type $G_2$. The minimal representation of $\mathbf{G}$, when restricted to…

Let G be a reductive group over a non-archimedean local field and let S(G) be its Schwartz algebra. We compare Ext-groups of tempered G-representations in several module categories: smooth G-representations, algebraic S(G)-modules,…

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation $\pi$ of a connected reductive $p$-adic group, subject to the assumption that $\pi$ is obtained via induction from a representation of…

We construct an infinite tower of irreducible calibrated representations of periplectic Brauer algebras on which the cup-cap generators act by nonzero matrices. As representations of the symmetric group, these are exterior powers of the…

Let $A$ be a finite dimensional associative algebra with derivations over a field of characteristic zero, i.e., an algebra whose structure is enriched by the action of a Lie algebra $L$ by derivations, and let $c_n^L(A),$ $n\geq 1,$ be its…

Let $F$ be a non-archimedean local field of characteristic zero. We study theta correspondence for (complex) representations of symplectic--even orthogonal dual reductive pairs over $F;$ more specifically, the big theta lifts. We prove…