The PBW Basis of $U_{q,\overline {q}}(\ddot {\mathfrak {g}\mathfrak {l}}

The PBW Basis of $U_{q,\overline {q}}(\ddot {\mathfrak {g}\mathfrak {l}}_{n})$

Published:2022-03-25 Issue: Volume: Page:
ISSN:1083-4362
Container-title:Transformation Groups
language:en
Short-container-title:Transformation Groups

Author:

Neguț Andrei^ORCID

Abstract

AbstractWe consider the PBW basis of the quantum toroidal algebra of

${\mathfrak {g}\mathfrak {l}}_{n}$

g l n , which was developed in Neguț (Adv. Math. 372, 2020), and prove commutation relations between its generators akin to the ones studied in Burban and Schiffmann (Duke Math. J. 161(7):1171–1231, 2012) for n = 1. This gives rise to a new presentation of the quantum toroidal algebra of type A.

Funder

Massachusetts Institute of Technology

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://link.springer.com/content/pdf/10.1007/s00031-022-09696-x.pdf

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