Journal article
The R-Matrix of the Quantum Toroidal Algebra Uq,t(gl. 1) in the Fock Module
A Garbali, J de Gier
Communications in Mathematical Physics | Published : 2021
Abstract
We propose a method to compute the R-matrix R on a tensor product of Fock modules from coproduct relations in a Hopf algebra. We apply this method to the quantum toroidal algebra Uq,t(gl. 1). We show that the coproduct relations of Uq,t(gl. 1) reduce to a single elegant equation for R. Using the theory of symmetric Macdonald polynomials we show that this equation provides a recursive formula for the matrix elements of R.
Grants
Awarded by Australian Research Council
Funding Acknowledgements
We gratefully acknowledge support from the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS). This project was supported in part by the ARC Discovery Grant DP190102897. A. G. would like to thank Jean-Emile Bourgine, Stephane Dartois, Matteo Mucciconi and Ole Warnaar for useful comments and discussions. We thank Andrei Okounkov and Olivier Schiffmann for comments and references and Andrei Negu and Andrey Smirnov for explaining their works.