Type: Seminar

Distribution: World

Expiry: 12 Sep 2008

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

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}).
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. |