Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A

Anthony Henderson

Abstract

The intersection cohomologies of closures of nilpotent orbits of linear (respectively, cyclic) quivers are known to be described by Kazhdan-Lusztig polynomials for the symmetric group (respectively, the affine symmetric group). We explain how to simplify this description using a combinatorial cancellation procedure, and derive some consequences for representation theory.

Keywords: intersection cohomology, cyclic quivers, Kazhdan-Lusztig polynomials.

AMS Subject Classification: Primary 17B37; secondary 05E15, 20C08.