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Statut Confirmé
Série STRINT
Domaines hep-th
Date Vendredi 9 Mars 2018
Heure 11:30
Institut LPTENS
Salle LPTENS Library
Nom de l'orateur Tsuboi
Prenom de l'orateur Zengo
Addresse email de l'orateur
Institution de l'orateur LPT ENS
Titre Quantum groups, Yang-Baxter maps and quasi-determinants
Résumé 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 we 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-Pl\"{u}cker 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. [Ref: arXiv:1708.06323 (Nucl. Phys. B 926 (2018) 200-238)]
Numéro de preprint arXiv 1708.06323
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