Reductive subgroups of reductive groups in nonzero characteristic

Abelian Unipotent Subgroups of Reductive Groups

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the “order formula” of D. Testerman for unipotent elements in G; moreover, we show that the same formula determines the p-nilpotence degree of the corresponding nilpotent elements in the Lie algebr...

Elementary Subgroups of Isotropic Reductive Groups

Let G be a not necessarily split reductive group scheme over a commutative ring R with 1. Given a parabolic subgroup P of G, the elementary group EP (R) is defined to be the subgroup of G(R) generated by UP (R) and UP−(R), where UP and UP− are the unipotent radicals of P and its opposite P −, respectively. It is proved that if G contains a Zariski locally split torus of rank 2, then the group E...

Computing Invariants of Reductive Groups in Positive Characteristic

This paper gives an algorithm for computing invariant rings of reductive groups in arbitrary characteristic. Previously, only algorithms for linearly reductive groups and for finite groups have been known. The key step is to find a separating set of invariants.

Reductive Groups

Representations of Reductive Groups

This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...