The quantum toroidal gl(1) (Evgeny Mukhin, Indiana University–Purdue University Indianapolis, IUPUI)

23.02.2023 14:15

The quantum toroidal gl(1) algebra appears in many areas of mathematics and physics. For example, it is isomorphic to the Hall algebra of the elliptic curve, it acts on equivariant K-theory of Hilbert scheme of points in C^2, it is a quantized version of W-algebra W_{1+\infty} in conformal field theory, it describes the action of Macdonald operators in the space of symmetric polynomials, etc.

In this talk we will give an introduction to the quantum toroidal gl(1) algebra and a review of various related results. Our motivation originates in the integrable model defined by the transfer matrices related to the R-matrix of this algebra. In some limit, some instances of this model recover quantum models related to affine W-algebras og gl(m|n) type and are expected to be dual to affine Gaudin models. In particular, it includes the quantum KdV flows.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Topologie et géométrie"

entrée libre