A note on Galois representations valued in reductive groups with open image

A Note on Galois Representations with Big Image

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...

Abelian Galois Cohomology of Reductive Groups

In this paper we introduce a new functor H ab(K,G) from the category of connected reductive groups over a field K of characteristic 0 to abelian groups. We call H ab(K,G) the first abelian Galois cohomology group of G. The abelian group H ab(K,G) is related to the pointed setH (K,G) by the abelianization map ab:H(K,G)→ H ab(K,G). When K is a local field or a number field, the map ab 1 is surjec...

Coisotropic Representations of Reductive Groups

A symplectic action G : X of an algebraic group S on a symplectic algebraic variety X is called coisotropic if a generic orbit of this action is a coisotropic submanifold of X. In this article a classification of coisotropic symplectic linear actions G : V is given in the case where G is a reductive group.

Whittaker Supports for Representations of Reductive Groups

Let F be either R or a finite extension of Qp, and let G be a finite central extension of the group of F -points of a reductive group defined over F . Also let π be a smooth representation of G (Fréchet of moderate growth if F = R). For each nilpotent orbit O we consider a certain Whittaker quotient πO of π. We define the Whittaker support WS(π) to be the set of maximal O among those for which ...