Lax operator for Macdonald symmetric functions

This is a joint work with Evgeny Sklyanin. Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q,t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the same variables and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of a Baker-Akhiezer function. It also provides a description of the stable non-negative spherical part of the the double affine Hecke algebra of type A.