Abstract
Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables \({x_{1},x_{2},{\ldots}}\) and of two parameters q, t are their eigenfunctions. We express our operators in terms of the Hall–Littlewood symmetric functions of the variables \({x_{1},x_{2},{\ldots}}\) and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of Baker–Akhiezer function.
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Nazarov, M., Sklyanin, E. Lax Operator for Macdonald Symmetric Functions. Lett Math Phys 105, 901–916 (2015). https://doi.org/10.1007/s11005-015-0770-1
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DOI: https://doi.org/10.1007/s11005-015-0770-1