Quantum toroidal and shuffle algebras
Representation Theory
2020-06-03 v5 Algebraic Geometry
Quantum Algebra
Abstract
In this paper, we prove that the quantum toroidal algebra of gl_n is isomorphic to the double shuffle algebra of Feigin and Odesskii for the cyclic quiver. The shuffle algebra viewpoint will allow us to prove a factorization formula for the universal R-matrix of the quantum toroidal algebra.
Cite
@article{arxiv.1302.6202,
title = {Quantum toroidal and shuffle algebras},
author = {Andrei Neguţ},
journal= {arXiv preprint arXiv:1302.6202},
year = {2020}
}
Comments
The previous version of this paper was broken into two parts: the present version contains the representation-theoretic half (to which we added a number of additional results) and the geometric half has been moved to arXiv:1811.01011