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arXiv · 1411.1315

Lax operator for Macdonald symmetric functions

Maxim Nazarov·Evgeny Sklyanin
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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.

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Maxim Nazarov, Evgeny Sklyanin. 2015-06-23. Lax operator for Macdonald symmetric functions. https://doi.org/10.1007/s11005-015-0770-1

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