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Decomposition numbers for perverse sheaves

Daniel Juteau (2009)

Annales de l’institut Fourier

The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial nilpotent orbit in a simple Lie algebra.This work has applications to modular representation theory, for Weyl groups using the nilpotent cone of the corresponding semisimple Lie algebra, and for reductive...

Decomposition of reductive regular Prehomogeneous Vector Spaces

Hubert Rubenthaler (2011)

Annales de l’institut Fourier

Let ( G , V ) be a regular prehomogeneous vector space (abbreviated to P V ), where G is a reductive algebraic group over . If V = i = 1 n V i is a decomposition of V into irreducible representations, then, in general, the PV’s ( G , V i ) are no longer regular. In this paper we introduce the notion of quasi-irreducible P V (abbreviated to Q -irreducible), and show first that for completely Q -reducible P V ’s, the Q -isotypic components are intrinsically defined, as in ordinary representation theory. We also show that, in an appropriate...

Decompositions of local rigid ACD groups

Adolf Mader, Otto Mutzbauer (2001)

Colloquium Mathematicae

We study direct decompositions of extensions of rigid completely decomposable groups by finite primary groups. These decompositions are unique and can be found by finite procedures. By passing to certain quotients the determination of the direct decompositions is made more efficient.

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