Anthony Henderson
(University of Sydney)
Friday 18th March, 12.0512.55pm, Carslaw 275
Equalities of KazhdanLusztig polynomials of type A
The KazhdanLusztig polynomials of the symmetric group have
many interpretations. Combinatorially, they are the solution
to a certain recurrence. Geometrically, they describe intersection
cohomology of Schubert varieties. Representationtheoretically,
they describe composition multiplicities of standard modules of
affine Hecke algebras. In this talk I will examine a phenomenon
in which certain KazhdanLusztig polynomials in different symmetric
groups are equal, sketching proofs from all three points of view.
The first two proofs generalize immediately to the affine symmetric
group; I will speculate on the possible implications for affine
Hecke algebras at a root of unity.
