The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
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University of Sydney Algebra Seminar

Anthony Henderson (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.