Categorification of a parabolic Hecke module via sheaves on moment graphs
arXiv:1208.1492 · 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) non-critical singular blocks of (a deformed version of) category , using indecomposable special modules over the structure algebra of the corresponding Bruhat graph.
26 pages, substantially revised version. To appear in Pac. J. Math