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