Algebraic Characters for Harish-Chandra modules

TL;DR

This paper develops a cohomological framework for character theory of (g,K)-modules, extending classical results to broader categories and applying it to discretely decomposable branching problems.

Contribution

It introduces a cohomological approach to (g,K)-module characters, broadening the scope beyond admissible modules and connecting to branching problem solutions.

Findings

Cohomological formalism extends Harish-Chandra's character theory.

Classical character results apply to larger categories of modules.

Algebraic characters effectively solve discretely decomposable branching problems.

Abstract

We give a cohomological treatment of a character theory for (g,K)-modules. This leads to a nice formalism extending to large categories of not necessarily admissible (g,K)-modules. Due to results of Hecht, Schmid and Vogan the classical results of Harish-Chandra's global character theory extend to this general setting. As an application we consider a general setup, for which we show that algebraic characters answer discretely decomposable branching problems.