Seminar talk, 20 November 2024, 16:00

Speaker: Yasushi Ikeda

Title: Quantum argument shifts in general linear Lie algebras

Abstract:
Argument shift algebras in $S(g)$ (where $g$ is a Lie algebra) are Poisson commutative subalgebras (with respect to the Lie-Poisson bracket), generated by iterated argument shifts of Poisson central elements. Inspired by the quantum partial derivatives on $U(gl_{d})$ proposed by Gurevich, Pyatov, and Saponov, I and Georgy Sharygin showed that the quantum argument shift algebras are generated by iterated quantum argument shifts of central elements in $U(gl_{d})$. In this talk, I will introduce a formula for calculating iterated quantum argument shifts and generators of the quantum argument shift algebras up to the second order, recalling the main theorem.