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A GRAPHICAL DESCRIPTION OF (Dn,An−1) KAZHDAN–LUSZTIG POLYNOMIALS

Published online by Cambridge University Press:  02 August 2012

TOBIAS LEJCZYK  and
CATHARINA STROPPEL
TOBIAS LEJCZYK
Affiliation:
Department of Mathematics, Endenicher Allee 60, 53115 Bonn, Germany e-mail: Lejczyk@math.uni-bonn.de
CATHARINA STROPPEL
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA e-mail: stroppel@uchicago.edu
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Abstract

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We give an easy diagrammatical description of the parabolic Kazhdan–Lusztig polynomials for the Weyl group Wn of type Dn with parabolic subgroup of type An and consequently an explicit counting formula for the dimension of morphism spaces between indecomposable projective objects in the corresponding category . As a by-product we categorify irreducible Wn-modules corresponding to the pairs of one-line partitions. Finally, we indicate the motivation for introducing the combinatorics by connections to the Springer theory, the category of perverse sheaves on isotropic Grassmannians, and to the Brauer algebras, which will be treated in two subsequent papers of the second author.

Keywords

17B1016G1005E15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 313 - 340
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

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