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Journal of Lie Theory 24 (2014), No. 4, 1161--1206
Copyright Heldermann Verlag 2014

Algebraic Characters of Harish-Chandra Modules

Fabian Januszewski
Karlsruher Institut für Technologie, Institut für Algebra und Geometrie, Kaiserstr. 89-93, 76133 Karlsruhe, Germany

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.

Keywords: Harish-Chandra modules, Lie algebra cohomology, algebraic characters, Blattner formulae, non-admissible branching laws, localization of Grothendieck groups.

MSC: 17B10, 17B55, 22E47

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