Tetrahedron Equation and Quantum R Matrices for Modular Double of Uq(D(2)        n+1), Uq(A(2)        2n) and Uq(C(1)        n)

Atsuo Kuniba; Masato Okado; Sergey Sergeev

doi:10.1007/s11005-015-0747-0

Tetrahedron Equation and Quantum R Matrices for Modular Double of U_q(D⁽²⁾ _n+1), U_q(A⁽²⁾ _2n) and U_q(C⁽¹⁾ _n)

Atsuo Kuniba^*, Masato Okado, Sergey Sergeev

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

We introduce a homomorphism from the quantum affine algebras U_q(D⁽²⁾ _n+1), U_q(A⁽²⁾ _2n), U_q(C⁽¹⁾ _n) to the n-fold tensor product of the q-oscillator algebra A_q. Their action commutes with the solutions of the Yang–Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of A_q. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.

Original language	English
Pages (from-to)	447-461
Number of pages	15
Journal	Letters in Mathematical Physics
Volume	105
Issue number	3
DOIs	https://doi.org/10.1007/s11005-015-0747-0
Publication status	Published - Mar 2015
Externally published	Yes

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title = "Tetrahedron Equation and Quantum R Matrices for Modular Double of Uq(D(2) n+1), Uq(A(2) 2n) and Uq(C(1) n)",

abstract = "We introduce a homomorphism from the quantum affine algebras Uq(D(2) n+1), Uq(A(2) 2n), Uq(C(1) n) to the n-fold tensor product of the q-oscillator algebra Aq. Their action commutes with the solutions of the Yang–Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of Aq. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.",

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T1 - Tetrahedron Equation and Quantum R Matrices for Modular Double of Uq(D(2) n+1), Uq(A(2) 2n) and Uq(C(1) n)

AU - Kuniba, Atsuo

AU - Okado, Masato

AU - Sergeev, Sergey

PY - 2015/3

Y1 - 2015/3

N2 - We introduce a homomorphism from the quantum affine algebras Uq(D(2) n+1), Uq(A(2) 2n), Uq(C(1) n) to the n-fold tensor product of the q-oscillator algebra Aq. Their action commutes with the solutions of the Yang–Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of Aq. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.

AB - We introduce a homomorphism from the quantum affine algebras Uq(D(2) n+1), Uq(A(2) 2n), Uq(C(1) n) to the n-fold tensor product of the q-oscillator algebra Aq. Their action commutes with the solutions of the Yang–Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of Aq. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras.

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KW - 81R50

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IS - 3

ER -

Tetrahedron Equation and Quantum R Matrices for Modular Double of U_q(D⁽²⁾ _n+1), U_q(A⁽²⁾ _2n) and U_q(C⁽¹⁾ _n)

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