Seminar Programme - Spring 2004

Thursday 16 January 2004

Abstract:
I will describe a presentation for certain algebras associated to a nilpotent matrices inside the Lie algebra $gl_N(C)$, showing quite surprisingly that these algebras are closely related to Drinfeld's Yangians. The definition of these algebras goes back to work of Kostant and Lynch in 1970s. However they were recently rediscovered and generalized to arbitrary nilpotent elements of arbitrary semisimple Lie algebras by Premet. The representation theory of these algebras is also extremely interesting, but I probably wont have time to say much about that...

Thursday 29 January 2004

Abstract:
For a finite subgroup G of SL(n,C) the McKay correspondence is a relationship between the G-equivariant geometry of C^n and the geometry of a 'crepant' resolution of the quotient singularity C^n/G. The talk will describe the classical case n=2, as understood in the 1980's in terms of K theory by Gonzalez-Sprinberg and Verdier, and also recent progress on the case n=3, now understood using the `modern' technology of derived categories.

Thursday 5 February 2004

Abstract:
In my talk I shall introduce the concept of G-completely reducible subgroups due to Serre. This notion faithfully generalizes the concept of semisimplicity from representation theory. It is part of a wider philosophy developed by Serre and others to extend result from representation theory to morphisms of algebraic groups. I shall explain this philosophy and Serre's notion and will outline some new results in the area. Among them is a joint result with B. Martin and M. Bate which shows that G-complete reducibility is equivalent to an earlier notion by R.W. Richardson. As a consequence we obtain an affirmative answer to a question of Serre on normal subgroups of G-completely reducible subgroups. In the special case G = GL(V) this result reduces to Clifford theory.

Thursday 12 February 2004

Abstract:
A "p-local finite group'' is an algebraic object which consists of a system of fusion data in a finite p-group S, as formalized by Ll. Puig, extended by some extra information contained in a category which allows rigidification of the fusion data. Such objects have ``classifying spaces'' which satisfy many of the homotopy theoretic properties of p-completed classifying spaces of finite groups. This talk is a survey of what is known so far about these p-local finite groups, and is intended as a friendly introduction to the subject. Time permitting, several central problems which are currently open will also be mentioned.

Thursday 19 February 2004

Abstract:
TBA

All meetings will take place at 4.00pm Thursdays in Lecture Room C on the ground floor of the Watson Building, unless otherwise stated. Visitors are welcome.

For further information please contact Dr G Röhrle (Tel: 0121 414 7374. Email: ger@for.mat.bham.ac.uk)

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