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.

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( slides | video )

Comments: Note the non-standard start time!

Geometry of differential equations seminar