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We study the interpolation Macdonald functions, remarkable inhomogeneousgeneralizations of Macdonald functions, and a sequence $A^1, A^2, \ldots$ ofcommuting operators that are diagonalized by them. Such a sequence of operatorsarises in the projective limit of finite families of commuting q-differenceoperators studied by Okounkov, Knop and Sahi. The main theorem is an explicitformula for the operators $A^k$. Our formula involves the family ofHall-Littlewood functions and a new family of inhomogeneous Hall-Littlewoodfunctions, for which we give an explicit construction and identify as adegeneration of the interpolation Macdonald functions in the regime $q\rightarrow 0$. This article is inspired by the recent papers ofNazarov-Sklyanin on Macdonald and Sekiguchi-Debiard operators, and our maintheorem is an extension of their results.

Interpolation Macdonald operators at infinity