Jun Hu (University of Sydney)

Friday 12th September, 12.05-12.55pm, Carslaw 159

On the decomposition numbers of the Hecke algebra of type D_n when n is even

Let n >= 4 be an integer and 1 < e < n an odd integer. Let q be a primitive e-th root of unity in a field K with char K not 2. In this talk, we shall consider the decomposition numbers of the Hecke algebra H_q(D_n) (over K) with parameter q. If n is odd, computing the decomposition numbers of H_q(D_n) is easily reduced to computing the decomposition numbers of the Hecke algebras H_q(A_m) for m <= n by a Morita equivalence result of Pallikaros. The main result in this talk is the determination of the decomposition numbers of H_q(D_n) in the case when n is even. We obtain some equalities over K which explicitly relate these decomposition numbers to the decomposition numbers of the Hecke algebras H_q(B_n) and H_q(A_m) for m <= n and the evaluation at q of certain Schur elements of the Hecke algebras H_q(A_n/2) and H_q(B_n).