A graphical description of $(D_n,A_{n-1})$ Kazhdan-Lusztig polynomials

Abstract

We give an easy diagrammatical description of the parabolic Kazhdan-Lusztig polynomials for the Weyl group $W_n$ of type $D_n$ with parabolic subgroup of type $A_n$ and consequently an explicit counting formula for the dimension of the morphism spaces between indecomposable projective objects in the corresponding category $Ø_0^\p$. As a byproduct we categorify irreducible $W_n$-modules corresponding to pairs of one-line partitions. Finally we indicate the motivation for introducing the combinatorics by connections to Springer theory, the category of perverse sheaves on isotropic Grassmannians and to Brauer algebras which will be treated in \cite{ES}.

arXiv commentThis is an extended version of the first author's diploma thesis submitted at Bonn university 2010

References in corpus (1)

• Gradings on walled Brauer algebras and Khovanov's arc algebra