A tale of two shuffle algebras
Quantum Algebra
2024-03-12 v4 Representation Theory
Abstract
As a quantum affinization, the quantum toroidal algebra is defined in terms of its "left" and "right" halves, which both admit shuffle algebra presentations. In the present paper, we take an orthogonal viewpoint, and give shuffle algebra presentations for the "top" and "bottom" halves instead, starting from the evaluation representation of the quantum affine group and its usual R-matrix. An upshot of this construction is a new topological coproduct on the quantum toroidal algebra which extends the Drinfeld-Jimbo coproduct on the horizontal quantum affine subalgebra.
Cite
@article{arxiv.1908.08395,
title = {A tale of two shuffle algebras},
author = {Andrei Neguţ},
journal= {arXiv preprint arXiv:1908.08395},
year = {2024}
}
Comments
24 figures