School of Mathematics and Statistics
Algebra Seminar
The University of Sydney
spcr
 

University of Sydney Algebra Seminar

 

Jun Hu (University of Sydney)

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

On the decomposition numbers of the Hecke algebra of type Dn 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 Hq(Dn) (over K) with parameter q. If n is odd, computing the decomposition numbers of Hq(Dn) is easily reduced to computing the decomposition numbers of the Hecke algebras Hq(Am) for m <= n by a Morita equivalence result of Pallikaros. The main result in this talk is the determination of the decomposition numbers of Hq(Dn) 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 Hq(Bn) and Hq(Am) for m <= n and the evaluation at q of certain Schur elements of the Hecke algebras Hq(An/2) and Hq(Bn).