XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018
VII School on Geometry and Physics 25-29.06.2018

Andrey Mironov

Commuting difference operators

We consider one–point commuting difference operators of rank one.
The coefficients of these operators depend on a functional parameter,
shift operators being included only with positive degrees. We
study these operators in the case of hyperelliptic spectral curve when
the marked point coincides with the branch point. We construct examples
of operators with polynomial and trigonometric coefficients.
Moreover, difference operators with polynomial coefficients can be embedded
in the differential ones with polynomial coefficients. This construction
provides a new way of constructing commutative subalgebras
in the first Weyl algebra. Results were obtained with G.Mauleshova.

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