Cherednik operators and Ruijsenaars-Schneider model at infinity

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JournalInternational Mathematics Research Notices
DateAccepted/In press - 7 Jul 2017
DateE-pub ahead of print - 21 Aug 2017
DatePublished (current) - 1 Apr 2019
Issue number8
Volume2019
Pages (from-to)2266–2294
Early online date21/08/17
Original languageEnglish

Abstract

Heckman introduced N operators on the space of polynomials in N
variables, such that these operators form a covariant set relative to permutations
of the operators and variables, and such that Jack symmetric polynomials are
eigenfunctions of the power sums of these operators. We introduce the analogues
of these N operators for Macdonald symmetric polynomials, by using Cherednik
operators. The latter operators pairwise commute, and Macdonald polynomials
are eigenfunctions of their power sums.We compute the limits of our operators at
N→∞. These limits yield a Lax operator for Macdonald symmetric functions.

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