Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 028, 9 pages      math.QA/0702676      http://dx.doi.org/10.3842/SIGMA.2007.028
Contribution to the Vadim Kuznetsov Memorial Issue

Bethe Ansatz for the Ruijsenaars Model of BC1-Type

Oleg Chalykh
School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Received December 14, 2006, in final form February 06, 2007; Published online February 22, 2007

Abstract
We consider one-dimensional elliptic Ruijsenaars model of type BC1. It is given by a three-term difference Schrödinger operator L containing 8 coupling constants. We show that when all coupling constants are integers, L has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This result generalizes the Bethe ansatz formulas known in the A1-case.

Key words: Heun equation; three-term difference operator; Bloch eigenfunction; spectral curve.

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