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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 92064, 31 pages
http://dx.doi.org/10.1155/IJMMS/2006/92064

Quantum curve in q-oscillator model

Department of Theoretical Physics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, ACT 0200, Australia

Received 16 February 2006; Accepted 9 May 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.