Speaker：Kailash C Misra（North Carolina State University）

Time：2025-5-22, 15:00

Location：Conference Room C416 at Administration Building at Haiyun Campus 

Abstract:

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.