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arXiv:solv-int/9710011 · Journal of Physics A Mathematical and General

A conjecturedR-matrix

Harry Whiting Braden

Published Feb 20, 1998• 8 citations
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Abstract

A new spectral parameter independent R -matrix (that depends on all of the dynamical variables) is proposed for the elliptic Calogero-Moser models. The necessary and sufficient conditions for the existence this R -matrix reduces to a determinantal equality involving elliptic functions. The required identity appears new and is still unproven in full generality; we present it as conjecture.

DOI
10.1088/0305-4470/31/7/008

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A new spectral parameter independent R -matrix (that depends on all of the dynamical variables) is proposed for the elliptic Calogero-Moser models. The necessary and sufficient conditions for the existence this R -matrix reduces to a determinantal equality involving elliptic functions. The required identity appears new and is still unproven in full generality; we present it as conjecture.
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On the RRR-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators
We propose and prove a set of identities for the elliptic GLMGL_MGLM​ RRR -matrix (in the fundamental representation). In the scalar case ( M=1M=1M=1 ), these are elliptic function identities derived by Ruijsenaars as necessary and sufficient conditions for his kernel identity underlying the construction of integral solutions of quantum spinless Ruijsenaars–Schneider model. In this respect, our result can be regarded as a first step toward constructing solutions of the quantum eigenvalue problem for the anisotropic spin Ruijsenaars model.
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