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Quantum curve in q -oscillator model

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  • S. Sergeev

Abstract

A lattice model of interacting q -oscillators, proposed by V. Bazhanov and S. Sergeev in 2005 is the quantum-mechanical integrable model in 2 + 1 dimensional space-time. Its layer-to-layer transfer matrix is a polynomial of two spectral parameters, it may be regarded in terms of quantum groups both as a sum of sl ( N ) transfer matrices of a chain of length M and as a sum of sl ( M ) transfer matrices of a chain of length N for reducible representations. The aim of this paper is to derive the Bethe ansatz equations for the q -oscillator model entirely in the framework of 2 + 1 integrability providing the evident rank-size duality.

Suggested Citation

  • S. Sergeev, 2006. "Quantum curve in q -oscillator model," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-31, August.
    • Handle: RePEc:hin:jijmms:092064
    DOI: 10.1155/IJMMS/2006/92064
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