English

Five-term relation and Macdonald polynomials

Combinatorics 2018-12-11 v2 Quantum Algebra Representation Theory

Abstract

The non-commutative five-term relation T1,0T0,1=T0,1T1,1T1,0T_{1,0} T_{0,1} = T_{0,1} T_{1,1} T_{1,0} is shown to hold for certain operators acting on symmetric functions. The "generalized recursion" conjecture of Bergeron and Haiman is a corollary of this result.

Keywords

Cite

@article{arxiv.1604.08655,
  title  = {Five-term relation and Macdonald polynomials},
  author = {Adriano Garsia and Anton Mellit},
  journal= {arXiv preprint arXiv:1604.08655},
  year   = {2018}
}

Comments

Some mistakes are corrected and the proof is substantially expanded. Accepted in JCTA

R2 v1 2026-06-22T13:44:07.173Z