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.

arXiv commentSignificant 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

References in corpus (1)

• Representations of quantum toroidal $g{l}_n$