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K-State Today

February 12, 2013

Mathematics Colloquium today

By Reta McDermott

Ting Xue from Northwestern University will present "Nilpotent Orbits and Springer Representations" at 2:30 p.m. Feb. 12 in 122 Cardwell Hall.

Abstract: 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 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. The Xue's work completes the theory of Springer correspondence by extending it to bad characteristics. A crucial ingredient in Xue's work on the Springer correspondence is the development of appropriate combinatorics for the classification of nilpotent orbits in bad characteristics.