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.