Forthcoming Seminars › Seminar Series

Representation Theory Seminar

Thu, 17/01/2008
13:30 		Steve Doty (Loyola) Representation Theory Seminar Add to calendar L3
Annihilators of permutation modules
The representation theory of symmetric groups starts with the permutation modules. It turns out that the annihilator of a permutation module can be described explicitly in terms of the combinatorics of Murphy's cellular basis of the group algebra of the symmetric group in question. In fact, we will show that the annihilator is always a cell ideal. This is recent joint work with K. Nyman.
Thu, 24/01/2008
13:30 		Johannes Siemons (East Anglia) Representation Theory Seminar Add to calendar L3
On a conjecture of Foulkes
For the integers $ a $ and $ b $ let $ P(a^b) $ be all partitions of the set $ N= {1,..., ab} $ into parts of size $ a. $ Further, let $ \mathbb{C}P (a^b) $ be the corresponding permutation module for the symmetric group acting on $ N. $ A conjecture of Foulkes says that $ \mathbb{C}P (a^b) $ is isomorphic to a submodule of $ \mathbb{C}P (b^a) $ for all $ a $ not larger than $ b. $ The conjecture goes back to the 1950's but has remained open. Nevertheless, for some values of $ b $ there has been progress. I will discuss some proofs and further conjectures. There is a close correspondence between the representations of the symmetric groups and those of the general linear groups, via Schur-Weyl duality. Foulkes' conjecture therefore has implications for $ GL $-representations. There are interesting connections to classical invariant theory which I hope to mention.
Thu, 31/01/2008
13:30 		Michael Wemyss (Bristol) Representation Theory Seminar Add to calendar L3
Reconstruction Algebras for two-dimensional quotient singularities
I will describe how to build a noncommutative ring which dictates the process of resolving certain two-dimensional quotient singularities. Algebraically this corresponds to generalizing the preprojective algebra of an extended Dynkin quiver to a larger class of geometrically useful noncommutative rings. I will explain the representation theoretic properties of these algebras, with motivation from the geometry.
Thu, 28/02/2008
13:30 		Nicolas Guay (Edinburgh) Representation Theory Seminar Add to calendar L3
Algebras and Lie algebras of double affine type

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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