Mathematics – Representation Theory
Scientific paper
2009-04-17
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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