Adjustment matrices

Abstract: James's Conjecture predicts that the adjustment matrix for weight $w$ blocks of the Iwahori-Hecke algebras $\mathcal{H}_{n}$ and the $q$-Schur algebras $\mathcal{S}_{n}$ is the identity matrix when $w<\textnormal{char}(\mathbb{F})$. Fayers has proved James's Conjecture for blocks of $\mathcal{H}_{n}$ of weights 3 and 4. We shall discuss some results on adjustment matrices that have been used to prove James's Conjecture for blocks of $\mathcal{S}_{n}$ of weights 3 and 4 in an upcoming paper. If time permits, we will look at a proof of the weight 3 case.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.