University of Sydney Algebra Seminar

Andrew Mathas (University of Sydney)

Friday 29 May, 12-1pm, Place: Carslaw 375

Fock spaces and Fayers' Conjecture

Matt Fayers has given an LLT-like algorithm for computing the graded decomposition numbers of the cyclotomic Hecke algebras. The main difficulties for this calculation centre around identifying the multipartitions that label the irreducible modules of the Hecke algebras. Fayers conjectured that the irreducible modules are precisely those for which the degree of certain parabolic Kazhdan-Lusztig polynomials is equal to the defect of the block. I will explain how to prove this result which, ultimately, follows from understanding the modules that can appear in the socle of the graded Weyl modules. This is joint work with Jun Hu.