James’s Conjecture predicts that the adjustment matrix for weight w blocks of the Iwahori-Hecke algebras ℋn and the q-Schur algebras 𝒮n is the identity matrix when w < char(𝔽). Fayers has proved James’s Conjecture for blocks of ℋn 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 𝒮n of weights 3 and 4 in an upcoming paper. If time permits, we will look at a proof of the weight 3 case.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
