MS Seminar (Mathematics - String Theory)

Speaker: Go Noshita (UTokyo)
Title: Quiver Quantum Toroidal Algebra and Crystal Representations
Date (JST): Tue, Feb 15, 2022, 14:00 - 15:30
Place: Zoom
Related File: 2769.pdf
Abstract: This talk is based on arxiv:2101.03953, 2108.07104, and 2109.02045. We propose a new class of algebras, Quiver Quantum Toroidal Algebra, which is a generalization of the quantum toroidal $\mathfrak{gl}_{1}$.
Similar to the quantum toroidal $\mathfrak{gl}_{1}$, the (shifted) quiver quantum toroidal algebra acts on general 1d, 2d, 3d crystals. We also study the way of constructing 2d crystal representations from 1d crystal representations.