Affine Lie algebras and crystal bases
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：Kailash C. Misra (North Carolina State University)
：2022-05-31 09:00
：Tencent Meeting/VOOV ID: 139-479-048 (No pwd)
Speaker：Kailash C. Misra (North Carolina State University)
Time: 2022-05-31,09:00 (Beijing Time)
Location:Tencent Meeting/VOOV ID: 139-479-048 (No pwd)
Abstract: Affine Lie algebras, also sometimes called current algebras are infinite dimensional analogs of finite dimensional semisimple Lie algebras. The representation theory of affine Lie algebras have applications in many areas of mathematics (such as: number theory, combinatorics, group theory, geometry, topology etc) and physics (such as: conformal field theory, integrable systems, statistical mechanics etc). To study the combinatorial properties of affine Lie algebra representations, Kashiwara and Lusztig independently introduced combinatorial objects called crystal bases associated with each irreducible integrable representation of an affine Lie algebra. In 1992, Misra et al introduced perfect crystals to give explicit realizations of the corresponding affine crystals. In 2000, Berenstein and Kazhdan introduced the notion of a geometric crystal whose ultra-discretization becomes an algebraic crystal. In this talk we will survey some of these developments and state some recent results.
About the Speaker：Kailash C. Misra received his Ph.D. in Mathematics from Rutgers University, NJ in 1982. He had postdoctoral appointments at University of Virginia during 1982-1984 and University of Wisconsin, Madison during 1984 -1986. Dr. Misra joined NCSU in Fall 1986 and was promoted to Associate Professor in 1991 and Full Professor in 1995. He received the NCSU Outstanding Teacher Award in 2004 and became a Fellow of the American Mathematical Society in 2014. Dr. Misra's current research interest is representation theory of Kac-Moody Lie algebras, Quantum groups and related topics.
