The PBW basis of $U_{q,\bar{q}}(\ddot{\mathfrak{gl}}_n)$

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.Comment: Significant enhancements over previous version. We give two orthogonal (in a certain sense) generators-and-relations presentations of the quantum toroidal algebr