Steinberg characters for Chevalley groups over finite local rings

Chevalley Groups over Commutative Rings

Chevalley Groups over Commutative Rings I. Elementary Calculations

This is the rst in a series of papers dedicated to the structure of Chevalley groups over commutative rings. The goal of this series is to systematically develop methods of calculations in Chevalley groups over rings, based on the use of their minimal modules. As an application we give new direct proofs for normality of the elementary subgroup, description of normal subgroups and similar result...

Orthogonal Groups over Local Rings

In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...

Characters of unipotent groups over finite fields

Let G be a connected unipotent group over a finite field Fq. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(Fq) and give an explicit description of L-packets in terms of the so-called “admissible pairs” for G. We then apply our results to show that if the centralizer of every geometric point of G is connected, then the dimension...

Characters of Reductive Groups over Finite Fields

Let E be a connected reductive algebraic group over C and let W be its Weyl group. The Springer correspondence allows us to parametrize the irreducible representations E of W as F = F^^ where u is a unipotent element in G (up to conjugacy) and <p is an irreducible representation of the group of components AH(u) = ZH(u)IZ°H(u). (However, not all <p arise in the parametrization.) For F = F^Uttp) ...