Crystal bases for reduced imaginary Verma modules of untwisted quantum affine algebras

：Kailash C Misra（美国North Carolina State University）
：2025-05-22 14:30
：海韵园行政楼C416

报告人：Kailash C Misra（美国North Carolina State University）

时  间：2025年5月22日14:30

地  点：海韵园行政楼C416

内容摘要:

Corresponding to the standard partition of the root system of an affine Lie algebra into set of positive and negative roots we have a standard Borel subalgebra from which we can induce the standard Verma modules. However, unlike for finite dimensional semisimple Lie algebras for an affine Lie algebra there exists other closed partitions of the root system which are not equivalent to the usual partition of the root system under the Weyl group action. Corresponding to such non-standard partitions we have non-standard Borel subalgebras from which one may induce other non-standard Verma modules and these typically contain both finite and infinite dimensional weight spaces. One such non-standard Verma module is called the imaginary Verma module. In this talk we will discuss the existence of imaginary crystal bases for the reduced imaginary Verma modules of untwisted quantum affine algebras. This talk is based on our recent joint work with Juan Arias and Vyacheslav.

个人简介：

Kailash C Misra is an Alumni Distinguished Graduate Professor of Mathematics at North Carolina State University (NCSU). He did his Ph.D. in Mathematics at Rutgers University in 1982. After two years of postdoc at University of Virginia and another two years at University of Wisconsin-Madison, he joined NCSU in 1986 as an Assistant Professor of Mathematics. In 1991 he was promoted to Associate Professor and in 1995 he was promoted to Full Professor. Professor Misra has been a Fellow of the American Mathematical Society since 2014. He has graduated 29 Ph.D. students from NCSU.

 

联系人：余铌娜