Representation theory of Hecke algebras and connections with Cherednik algebras (NAGRT)
Maria Chlouveraki (Université Versailles/Saint Quentin-en-Yvelines)
MSRI: Simons Auditorium
Hecke algebras associated with Weyl groups appear naturally as endomorphism rings in the study of finite reductive groups. Broué, Malle and Rouquier have generalized their definition to all complex reflection groups. Hecke algebras depend on a parameter q and their representation theory becomes very interesting when q specializes to a root of unity. The existence of canonical basic sets and the cellular algebra structure have been key elements in the understanding of the representation theory of Hecke algebras in that case. An open question is whether these structures exist for any choice of parameters and for all complex reflection groups. In this talk will see how the connections with the representation theory of rational Cherednik algebras, another type of algebras associated with complex reflection groups, could provide an answer to this problem.