Oberseminar
zur
Algebra und Algebraischen Kombinatorik
Dr. Ehud Meir
(University of Aberdeen)
The representation theory of the general linear
groups over finite local rings
Letkbe a finite field. The complex representation theory of the groupsGLn(k)was studied by Bernstein
and Zelevinsky. Instead of studying the representation theory of each group separately, they studied
them together using Harish-Chandra induction and restriction functors. This furnishes a structure
of a positive self adjoint Hopf algebra (or PSH-algebra) on the direct sum of the character groups,
and enables to reduce the representation theory of these groups to the study of the so called cuspidal
representations and the representation theory of the symmetric groups.
In this talk I will describe a work towards an extension of this theory to the representation theory
ofGLn(R), whereRis a finite quotient of a discrete valuation ring (e.g.R=Z=p
r
Zork[x]=(x
r
)). The
representation theory of such groups arise naturally when one studies representations of groups such
asGLn(Z)andGLn(Zp)(the p-adic integers). I will explain why the direct generalization of the Harish-
Chandra functors does not work, and what alternatives are conjectured to fill in this gap. This talk is
based on a joint work with Tyrone Crisp and Uri Onn.
Dienstag 02.02.2021
ab 16:00 Uhr
In StudIP, per BBB im e-a410
Alle Interessierten sind herzlich eingeladen.
Institut für Algebra, Zahlentheorie
und Diskrete Mathematik