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arXiv · 1208.1492

Categorification of a parabolic Hecke module via sheaves on moment graphs

Martina Lanini
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Abstract

We investigate certain categories, associated by Fiebig with the geometric representation of a Coxeter system, via sheaves on Bruhat graphs. We modify Fiebig's definition of translation functors in order to extend it to the singular setting and use it to categorify a parabolic Hecke module. As an application we obtain a combinatorial description of indecomposable projective objects of (truncated) non-critical singular blocks of (a deformed version of) category $\mathcal{O}$, using indecomposable special modules over the structure algebra of the corresponding Bruhat graph.

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Martina Lanini. 2012-08-07. Categorification of a parabolic Hecke module via sheaves on moment graphs. https://doi.org/10.2140/pjm.2014.271.415

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