|Title:||Nilpotent orbits and Springer representations|
|Speaker:||Ting Xue (University of Helsinki)|
Representation theory is connected to various areas of mathematics, such as harmonic analysis, mathematical physics, and number theory. 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 characteristics 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. Our work completes the theory of Springer correspondence by extending it to bad characteristics. A crucial ingredient in our work on the Springer correspondence is the development of appropriate combinatorics for the classification of nilpotent coadjoint orbits in bad characteristics.