OIST Representation Theory Seminar

Speaker: Aaron Yi Rui Low, National University of Singapore

Title: 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 $w<\mathrm{char}(\mathbb{F})$. 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.

Zoom info can be found on the seminar webpage.