EVENT DETAILS AND ABSTRACT

Title: Nilpotent orbits and the Springer correspondence
Speaker: Ting Xue
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Abstract:

In the geometric approach to the representation theory of reductive algebraic groups, some geometric objects are important in different contexts and the Springer theory always occurs. The theory works uniformly for Lie algebras over complex numbers and in finite characteristic except for certain small primes; these small primes are traditionally called bad. It is important to understand the theory at all primes, for example, for the purposes of number theory. Via an explicit geometric construction, the Springer correspondence relates nilpotent orbits in the Lie algebra of a connected reductive algebraic group to irreducible representations of its Weyl group. We describe the theory of Springer correspondence in bad characteristics. A crucial ingredient in our work on the Springer correspondence is the development of appropriate combinatorics for the classification of nilpotent orbits in bad characteristics.