Commuting matrix discrete operators and algebraic curves

A. F. Gundareva^ab, G. S. Mauleshova^ba, A. E. Mironov<sup>ab

a</sup> Novosibirsk State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: In this paper, we find spectral data for commuting discrete operators with matrix coefficients. The common eigenfunctions of the operators are rational functions on the spectral curve with certain special divisors of zeros and poles. Explicit examples are provided in the case of the elliptic spectral curve.

Key words and phrases: commuting discrete operators.

UDC: 517.929.2

Received: 22.12.2025