Projects per year
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.
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.
| Original language | English |
|---|---|
| Article number | IMRN-2017-186.R1 |
| Pages (from-to) | 2266–2294 |
| Journal | International Mathematics Research Notices |
| Volume | 2019 |
| Issue number | 8 |
| Early online date | 21 Aug 2017 |
| DOIs | |
| Publication status | Published - 1 Apr 2019 |
Bibliographical note
© The Author(s) 2017. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for detailsProfiles
Projects
- 2 Finished
-
Cherednik Algebras and Affine Lie Algebras
1/10/16 → 31/03/19
Project: Research project (funded) › Research
-
Cherednik Algebras at Infinity
Nazarov, M. L. & Balagovic, M.
1/10/11 → 31/10/14
Project: Research project (funded) › Research