# Exposé d'Emily Norton (Clermont-Ferrand) : Calibrated representations of cyclotomic Hecke algebras at roots of unity

30 September 2021
Saint-Etienne (Métare)
Europe/Paris timezone
Title: Calibrated representations of cyclotomic Hecke algebras
at roots of unity

Abstract: The cyclotomic Hecke algebra is a "higher level" version
of the Iwahori-Hecke algebra of the symmetric group. It depends on
a collection of parameters, and its combinatorics involves
multipartitions instead of partitions. We are interested in the case
when the parameters are roots of unity. In general, we cannot hope
for closed-form character formulas of the irreducible representations.
However, a certain type of representation called "calibrated" is
more tractable: those representations on which the Jucys-Murphy
elements act semisimply. We classify the calibrated representations
in terms of their Young diagrams, give a multiplicity-free formula
for their characters, and homologically construct them via BGG
resolutions. This is joint work with Chris Bowman and José Simental.

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Europe/Paris
Saint-Etienne (Métare)
C112