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ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Models solvable by Bethe Ansatz 1

Petr P. KULISH*

St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia

*Corresponding Author:
Petr P. KULISH
St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27
191023 St. Petersburg, Russia
E-mail: [email protected]

Received date: December 20, 2007; Revised date: March 10, 2008

Abstract

Diagonalization of integrable spin chain Hamiltonians by the quantum inverse scattering method gives rise to the connection with representation theory of different (quantum) algebras. Extending the Schur-Weyl duality between sl2 and the symmetric group SN from the case of the isotropic spin 1/2 chain (XXX-model) to a general spin chains related to the Temperley-Lieb algebra TLN(q) one finds a new quantum algebra Uq(n) with the representation ring equivalent to the sl2 one.

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