Cherednik operators at infinity (Maxim Nazarov, University of York)

20.03.2018 15:30

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. Then we compute the limits of our operators at $N\to\infty$. These limits yield a Lax operator for Macdonald symmetric functions. This is a joint work with Evgeny Sklyanin.

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Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

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