The category $\mathcal{O}$ for a general Coxeter system

Details The category $\mathcal{O}$ for a general Coxeter system The category $\mathcal{O}$ for a general Coxeter system

2009-04-17

arxiv.org/abs/0904.2734v1

Mathematics

Representation Theory

21 pages

Scientific paper

We study the category $\mathcal{O}$ for a general Coxeter system using a
formulation of Fiebig. The translation functors, the Zuckerman functors and the
twisting functors are defined. We prove the fundamental properties of these
functors, the duality of Zuckerman functor and generalization of Verma's result
about homomorphisms between Verma modules.

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