Seminar talk, 20 November 2024, 16:00

Speaker: Yasushi Ikeda

Title: Quantum argument shifts in general linear Lie algebras

Abstract:
Argument shift algebras in Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S(g)} (where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.