The PBW basis of $U_{q,\bar{q}}(\ddot{\mathfrak{gl}}_n)$
Quantum Algebra
2023-08-21 v3 Combinatorics
Representation Theory
Abstract
We consider the PBW basis of the type A quantum toroidal algebra developed by the author, and prove commutation relations between its generators akin to the ones studied by Burban-Schiffmann for n=1. This gives rise to a new presentation of the quantum toroidal algebra of type A.
Cite
@article{arxiv.1905.06277,
title = {The PBW basis of $U_{q,\bar{q}}(\ddot{\mathfrak{gl}}_n)$},
author = {Andrei Neguţ},
journal= {arXiv preprint arXiv:1905.06277},
year = {2023}
}
Comments
Significant enhancements over previous versions. We give two orthogonal (in a certain sense) generators-and-relations presentations of the quantum toroidal algebra. Improved presentation, with road map provided for each Section