SMS scnews item created by Anthony Henderson at Mon 1 Sep 2008 1448
Type: Seminar
Distribution: World
Expiry: 12 Sep 2008
Calendar1: 12 Sep 2008 1205-1255
CalLoc1: Carslaw 159
CalTitle1: Algebra Seminar: Hu -- On the decomposition numbers of the Hecke algebra of type D_n when n is even
Auth: anthonyh@asti.maths.usyd.edu.au

Algebra Seminar

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

Jun Hu

12th September, 12:05-12:55pm, Carslaw 159


Abstract

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).


After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

Anthony Henderson anthonyh@maths.usyd.edu.au.



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