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[Lecture] Sino-Russian Mathematics Center-JLU Colloquium(2022-013)
Jun. 17, 2022

Title: Factorization of Shapovalov elements

Speaker: Andrey Mudrov, MIPT, University of Leicester

Time: 15:00-17:00 pm, June 17, 2022 GMT+8

Venue: Zoom Meeting ID: 862 062 0549 Password: 2022


A classical result of J. Bernstein, I. Gelfand and S. Gelfand says that a singular vector in a Verma module over a simple complex Lie algebra can be obtained from its highest vector by applying a product of special elements of the negative nilpotent subalgebra called Shapovalov elements. We provide explicit formulas for those elements, and hence for singular vectors of the Verma modules, expressing them through certain matrix elements of the inverse contravariant Shapovalov form.


The speaker is currently an Associate Professor and a Senior Researcher at the Center of Fundamental Mathematics in MIPT, and an Honorary Lecturer at the University of Leicester. He is specializing in quantum groups, deformation quantization and related topics.