English

Lax operator for Macdonald symmetric functions

Exactly Solvable and Integrable Systems 2020-11-06 v3 Combinatorics Quantum Algebra Representation Theory

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,tq,t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the same variables and of the parameter tt corresponding to the partitions with one part only. Our expression is based on the notion of Baker-Akhiezer function.

Keywords

Cite

@article{arxiv.1411.1315,
  title  = {Lax operator for Macdonald symmetric functions},
  author = {Maxim Nazarov and Evgeny Sklyanin},
  journal= {arXiv preprint arXiv:1411.1315},
  year   = {2020}
}

Comments

14 pages, final version

R2 v1 2026-06-22T06:49:12.067Z