Representation Theory Seminar
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Thu, 16/10/2008 14:30 |
Petter Bergh (Trondheim / Oxford) |
Representation Theory Seminar  |
L3 |
| In 1989, Happel raised the following question: if the Hochschild cohomology groups of a finite dimensional algebra vanish in high degrees, then does the algebra have finite global dimension? This was answered negatively in a paper by Buchweitz, Green, Madsen and Solberg. However, the Hochschild homology version of Happel's question, a conjecture given by Han, is open. We give a positive answer to this conjecture for local graded algebras, Koszul algebras and cellular algebras. The proof uses Igusa's formula for relating the Euler characteristic of relative cyclic homology to the graded Cartan determinant. This is joint work with Dag Madsen. | |||
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Thu, 23/10/2008 14:30 |
Susanne Danz (Oxford) |
Representation Theory Seminar |
L3 |
| We consider the symmetric group S_n of degree n and an algebraically closed field F of prime characteristic p. As is well-known, many representation theoretical objects of S_n possess concrete combinatorial descriptions such as the simple FS_n-modules through their parametrization by the p-regular partitions of n, or the blocks of FS_n through their characterization in terms of p-cores and p-weights. In contrast, though closely related to blocks and their defect groups, the vertices of the simple FS_n-modules are rather poorly understood. Currently one is far from knowing what these vertices look like in general and whether they could be characterized combinatorially as well. In this talk I will refer to some theoretical and computational approaches towards the determination of vertices of simple FS_n-modules. Moreover, I will present some results concerning the vertices of certain classes of simple FS_n-modules such as the ones labelled by hook partitions or two part partitions, and will state a series of general open questions and conjectures. | |||
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Thu, 30/10/2008 14:30 |
Rudolf Tange (York) |
Representation Theory Seminar |
L3 |
| It is well-known that there is a strong link between the representation theories of the general linear group and the symmetric group over the complex numbers. J.A.Green has shown that this in also true over infinite fields of positive characteristic. For this he used the Schur functor as introduced by I.Schur in his PhD thesis. In this talk I will show that one can do the same thing for the symplectic group and the Brauer algebra. This is joint work with S.Donkin. As a consequence we obtain that (under certain conditions) the Brauer algebra and the symplectic Schur algebra in characteristic p have the same block relation. Furthermore we obtain a new proof of the description of the blocks of the Brauer algebra in characteristic zero as obtained by Cox, De Visscher and Martin. | |||
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Thu, 06/11/2008 14:30 |
Max Neunhoeffer (St Andrews) |
Representation Theory Seminar |
L3 |
| In this talk we present a new construction of a Wedderburn basis for the generic q-Schur algebra using the Du-Kazhdan-Lusztig basis. We show that this gives rise to a new view on the Du-Lusztig homomorphism to the asymptotic algebra. At the end we explain a potential plan for an attack on James' conjecture using a reformulation by Meinolf Geck. The talk starts with a gentle recollection of facts about Iwahori-Hecke-Algebras of type A and q-Schur algebras and aims to be accessible to people who are not (yet) experts in the representation theory of q-Schur algebras. All this is joint work with Olivier Brunat (Bochum). | |||
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Thu, 20/11/2008 14:30 |
Reidun Twarock (York) |
Representation Theory Seminar |
L3 |
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Thu, 04/12/2008 14:30 |
Nadia Mazza (Lancaster) |
Representation Theory Seminar |
L3 |
| This is joint work with Diaz, Glesser and Park. In Proc. Instructional Conf, Oxford 1969, G. Glauberman shows that several global properties of a finite group are determined by the properties of its p-local subgroups for some prime p. With Diaz, Glesser and Park, we reviewed these results by replacing the group by a saturated fusion system and proved that the ad hoc statements hold. In this talk, we will present the adapted versions of some of Glauberman and Thompson theorems. | |||
