(University of Sydney)
Friday 18th March, 12.05-12.55pm, Carslaw 275
Equalities of Kazhdan-Lusztig polynomials of type A
The Kazhdan-Lusztig 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. Representation-theoretically,
they describe composition multiplicities of standard modules of
affine Hecke algebras. In this talk I will examine a phenomenon
in which certain Kazhdan-Lusztig 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.