International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 11, Pages 92064, 31 p.
doi:10.1155/IJMMS/2006/92064
Quantum curve in q-oscillator model
S. Sergeev
Department of Theoretical Physics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra 0200, ACT, Australia
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.