Abstract:
For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation RLL=LLR, taking the trace of the L-operator gives a set of commuting difference operators. We show that for the above mentioned L-operator this approach gives Macdonald type operators with elliptic theta function coefficient, actually equivalent to Ruijsenaars' operators. The relationship between the difference L-operator and Krichever's Lax matrix is given, and an explicit formula for elliptic commuting differential operators is derived. We also study the invariant subspace for the system which is spanned by symmetric theta functions on the weight space.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 27 December 1995 / Accepted: 11 November 1996
Rights and permissions
About this article
Cite this article
Hasegawa, K. Ruijsenaars' Commuting Difference Operators as Commuting Transfer Matrices . Comm Math Phys 187, 289–325 (1997). https://doi.org/10.1007/s002200050137
Issue Date:
DOI: https://doi.org/10.1007/s002200050137