The (glm, gln) Duality in the Quantum Toroidal Setting

B. Feigin; M. Jimbo; E. Mukhin

doi:10.1007/s00220-019-03405-8

The (gl_m, gl_n) Duality in the Quantum Toroidal Setting

B. Feigin, M. Jimbo, E. Mukhin

Research output: Contribution to journal › Article › peer-review

Abstract

On a Fock space constructed from mn free bosons and lattice Z_mn, we give a level n action of the quantum toroidal algebra E_m associated to gl_m, together with a level m action of the quantum toroidal algebra E_n associated to gl_n. We prove that the E_m transfer matrices commute with the E_n transfer matrices after an appropriate identification of parameters.

Original language	English
Pages (from-to)	455-481
Number of pages	27
Journal	Communications in Mathematical Physics
Volume	367
Issue number	2
DOIs	https://doi.org/10.1007/s00220-019-03405-8
State	Published - Apr 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s00220-019-03405-8

Cite this

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abstract = "On a Fock space constructed from mn free bosons and lattice Zmn, we give a level n action of the quantum toroidal algebra Em associated to glm, together with a level m action of the quantum toroidal algebra En associated to gln. We prove that the Em transfer matrices commute with the En transfer matrices after an appropriate identification of parameters.",

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