The Argument Shift Method in Universal Enveloping Algebra Ugl_d
Time: 2023-09-25
Published By: Wenqiong Li
Speaker(s): Georgy Igorevich Sharygin (Moscow State University)
Time: 14:00-15:00 September 26, 2023
Venue: Room 29, Quan Zhai, BICMR
We prove the conjecture that allows one extend the argument shifting procedure from symmetric algebra Sgl_d of the Lie algebra gl_d to the universal enveloping algebra Ugl_d. Namely, it turns out that the iterated quasi-derivations of the central elements in Ugl_d commute with each other. Here quasi-derivation is a linear operator on Ugld, constructed by Gurevich, Pyatov and Saponov. This allows one better understand the structure of the quantum argument shift algebras (or the quantum Mishchenko-Fomenko algebras) in the universal enveloping algebra of gl_d. In the end I will briefly describe the methods that allow one to partially extend this result to other classical series of simple Lie algebras. Based on a joint work with Y. Ikeda and A. Molev.
