Relativistic Interacting Integrable Elliptic Tops

Abstract

We propose a relativistic generalization of integrable systems describing M interacting elliptic gl(N) Euler-Arnold tops. The obtained models are elliptic integrable systems that reproduce the spin elliptic GL(M) Ruijsenaars-Schneider model with N = 1 and relativistic integrable GL(N) elliptic tops with M = 1. We construct the Lax pairs with a spectral parameter on the elliptic curve.