The Symmetric Group Representation on Cohomology of the Regular Elements of a Maximal Torus of the Special Linear Group

Distinguished positive regular representations

Let $G$ be a tamely ramified reductive $p$-adic‎ ‎group‎. ‎We study distinction of a class of irreducible admissible representations‎ ‎of $G$ by the group of fixed points $H$ of an involution‎ ‎of $G$‎. ‎The representations correspond to $G$-conjugacy classes of‎ ‎pairs $(T,phi)$‎, ‎where $T$ is a‎ ‎tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter‎ ‎of $T$ whose restriction t...

Endoscopy and the cohomology of $GL(n)$

Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field‎. ‎Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...

Monomial Irreducible sln-Modules

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

On the Restriction of Characters of Special Linear Groups of Dimension Three

Cyclotomic structures on root lattices

The centralizer C(w) of an element w in a Weyl group W plays an important role in the structure and representation theory of split reductive groups G over finite and p-adic fields k, where W is the absolute Weyl group of G. If k is finite, this is well-known: the element w determines a maximal ktorus Tw ⊂ G and C(w) may be identified with the k-rational points in the Weyl group W (Tw, G) of Tw ...