The R-matrix of the quantum toroidal algebra
Andrei Negu\c{t}
TL;DR
This paper explores the R-matrix of the quantum toroidal algebra of type gl_1, providing a survey of its theoretical framework and explicit formulas through elliptic Hall and shuffle algebra perspectives.
Contribution
It offers a comprehensive survey and explicit formulas for the R-matrix of the quantum toroidal algebra of type gl_1, connecting it with elliptic Hall and shuffle algebras.
Findings
Explicit formulas for the R-matrix derived
Connections established with elliptic Hall algebra
Insights into Fock space representations
Abstract
We consider the R-matrix of the quantum toroidal algebra of type 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 show how to obtain certain explicit formulas.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Random Matrices and Applications