The R-matrix of the quantum toroidal algebra

Andrei Neguţ

doi:10.1215/21562261-2022-0030

Abstract

We consider the R-matrix of the quantum toroidal algebra of type ${\mathfrak{gl}_{1}}$ , both abstractly and in Fock space representations. We provide a survey of a certain point of view on this object which involves the elliptic Hall and shuffle algebras, and we show how to obtain certain explicit formulas.

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Andrei Neguţ. "The R-matrix of the quantum toroidal algebra." Kyoto J. Math. 63 (1) 23 - 49, February 2023. https://doi.org/10.1215/21562261-2022-0030

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Received: 22 July 2020; Revised: 14 January 2021; Accepted: 22 February 2021; Published: February 2023

First available in Project Euclid: 29 November 2022

MathSciNet: MR4593187

Digital Object Identifier: 10.1215/21562261-2022-0030

Subjects:

Primary: 17B37

Keywords: quantum toroidal algebra , R-matrix

Abstract

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