Journal
NUCLEAR PHYSICS B
Volume 926, Issue -, Pages 200-238Publisher
ELSEVIER
DOI: 10.1016/j.nuclphysb.2017.11.005
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Funding
- Australian Research Council
- CNRS
- European Research Council (Programme Ideas) [ERC-2012-AdG 320769 AdS-CFT-solvable]
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For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum Yang-Baxter map, which satisfies the set-theoretic Yang-Baxter equation. The map has a zero curvature representation among L-operators defined as images of the universal R-matrix. We find that the zero curvature representation can be solved by the Gauss decomposition of a product of L-operators. Thereby obtained a quasi-determinant expression of the quantum Yang-Baxter map associated with the quantum algebra U-q(gl(n)). Moreover, the map is identified with products of quasi-Plucker coordinates over a matrix composed of the L-operators. We also consider the quasi-classical limit, where the underlying quantum algebra reduces to a Poisson algebra. The quasi-determinant expression of the quantum Yang-Baxter map reduces to ratios of determinants, which give a new expression of a classical Yang-Baxter map. (C) 2017 The Author(s). Published by Elsevier B.V.
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