The defect of blocks in Hecke algebras

Abstract: When an algebra is not semisimple, a good way to understand its representation theory is through the study of its blocks. To each simple module in a block we can attach a numerical datum, which measures the complexity of the block: the defect. This is true for the symmetric group algebra, as well as its generalisations, the Iwahori-Hecke algebra of type A and the Ariki-Koike algebra. In a joint work with Nicolas Jacon we have proved, using algebraic combinatorics, that the defect is a block invariant for Ariki-Koike algebras, thus proving a conjecture formulated by Geck 30 years ago. In this talk we will present our proof, as well as our data indicating that this fact is true for all Hecke algebras associated with complex reflection groups.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar