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Lax operator for Macdonald symmetric functions (1411.1315v3)
Published 5 Nov 2014 in nlin.SI, math.CO, math.QA, and math.RT
Abstract: 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 Baker-Akhiezer function.