Titles and abstracts

Gwyn Bellamy: Cherednik algebras and projective Hecke algebras.


The purpose of this talk is to introduce sheaves of Cherednik algebras on projective space and explain their relationship with the projective Hecke algebra. Namely, I will describe how the KZ-functor relates modules for Cherenik algebra with modules for the projective Hecke algebra. This is based on joint work with Alexander Forbes.

Maria Chlouveraki: Yokonuma-Hecke algebras and knot invariants

Yokonuma-Hecke algebras were introduced by Yokonuma in the 1960’s in the context of Chevalley groups, as generalisations of Iwahori-Hecke algebras. They can also be defined independently as deformations of group algebras of complex reflection groups. Recently, they have been used by Juyumaya and Lambropoulou for the construction of invariants for framed and classical knots. In this talk, we will discuss some interesting developments in the study of these algebras, from both an algebraic and a topological point of view.

Eugenio Giannelli : On signed Young modules

In this talk, I will introduce signed Young permutation modules and I will describe the main properties of this family of modules of the symmetric group. In the second part of the talk I will present some new results on the modular structure of these modules. In particular I will describe some reduction formulas for signed p-Kostka numbers, namely the multiplicities of indecomposable signed Young modules as direct summands of signed Young permutation modules. This is joint work with Kay Jin Lim and Mark Wildon.

Nicolas Jacon: On the one dimensional representations of Hecke algebras

Recently Meinolf Geck has shown that a natural question concerning the parametrisation of the socle of the Steinberg representation for finite group of Lie type reduces to a natural question around the parametrisation of the one dimensional representations of Hecke algebras at roots of 1. We here show how we can find these parametrisations in the wider context of Ariki-Koike algebras. 

Liron Speyer: Kleshchev's decomposition numbers for cyclotomic Hecke algebras.

I will present recent joint work with Chris Bowman in which we calculate decomposition numbers for cyclotomic Hecke algebras. I will introduce the combinatorics underlying Webster's diagrammatic Cherednik algebra and its cellular structure, and discuss how we used isomorphisms between different subquotients to generalise the results of Chuang, Kleshchev, Tan and Teo on decomposition numbers. Our results on graded decomposition numbers take these level 1 results into higher levels and beyond, and apply over fields of arbitrary characteristic.

Louise Sutton: Graded decomposition numbers for Specht modules labelled by hook partitions

In 2008, Brundan, Kleshchev and Wang showed that Specht modules over cyclotomic Hecke algebras are gradable.  Firstly, I will discuss the grading on these modules together with results on graded dimensions of certain Specht modules, in particular,  those indexed by hook partitions. Using these formulae, I will  then discuss an alternative proof of Chuang, Miyachi and Tan's result on the graded decomposition numbers of these particular Specht modules in level 1, with the hope of extending this result to higher levels.

Michela Varagnolo: Categorical actions on unipotents representations of finite unitary groups.

I will report on a joint paper with O. Dudas and E. Vasserot. Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups (in non defining characteristic). The decategorification representation is isomorphic to a direct sum of level 2 Fock spaces. We deduce a conjecture by Gerber-Hiss-Jacon: the Harish Chandra branching graph
coincide with the crystal graph of these Fock spaces.