Categorification of a parabolic Hecke module via sheaves on moment graphs

Martina Lanini

Vol. 271 (2014), No. 2, 415–444

DOI: 10.2140/pjm.2014.271.415

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) noncritical singular blocks of (a deformed version of) category $\mathcal{O}$, using indecomposable special modules over the structure algebra of the corresponding Bruhat graph.

Keywords

sheaves on moment graphs, parabolic Hecke module

Mathematical Subject Classification 2010

Primary: 17B67, 20C08

Milestones

Received: 2 June 2013

Revised: 25 July 2013

Accepted: 25 August 2013

Published: 20 September 2014