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Lax operator for Macdonald symmetric functions

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JournalLetters in Mathematical Physics
DateE-pub ahead of print - 12 Jun 2015
DatePublished (current) - Jul 2015
Issue number7
Volume105
Pages (from-to)901-916
Early online date12/06/15
Original languageEnglish

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 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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© Springer Science+Business Media Dordrecht 2015. This is an author produced version of a paper published in Letters in Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy.

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