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

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 tr...

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Veröffentlicht in:	Communications in mathematical physics 2019-04, Vol.367 (2), p.455-481
Hauptverfasser:	Feigin, B., Jimbo, M., Mukhin, E.
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Sprache:	eng
Schlagworte:	Bosons Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Parameter identification Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical Transfer matrices
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description	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.
doi_str_mv	10.1007/s00220-019-03405-8
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subjects	Bosons Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Parameter identification Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical Transfer matrices
title	The (glm,gln) Duality in the Quantum Toroidal Setting
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