Elliptic quantum groups and Ruijsenaars models

Abstract

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups $E_{τ,η}(gl_N)$. The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.

15 pages, latex