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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. |