Bethe Ansatz for the Ruijsenaars Model of BC_1-Type

Details Bethe Ansatz for the Ruijsenaars Model of BC_1-Type Bethe Ansatz for the Ruijsenaars Model of BC_1-Type

2007-02-22

arxiv.org/abs/math/0702676v1

SIGMA 3 (2007), 028, 9 pages

Mathematics

Quantum Algebra

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.028

We consider one-dimensional elliptic Ruijsenaars model of type $BC_1$. It is
given by a three-term difference Schr\"odinger 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 $A_1$-case.

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