Some infinite dimensional representations of reductive groups with Frobenius maps

Infinite-dimensional Representations of Real Reductive Groups

is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...

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...

Infinite Dimensional Groups, Their Representations, Orbits, Invariants

1. Representation theory for infinite dimensional groups does not exist as a theory although such groups occur long ago in several branches of mathematics and its applications. Among the most important examples are: (a) groups of automorphisms of infinite dimensional vector spaces with some additional structures (unitary, symplectic, Fredholm etc.); (b) groups of diffeomorpliisms of smooth mani...

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.

Irreducible Representations of Infinite-dimensional Transformation Groups and Lie Algebras