Five-term relation and Macdonald polynomials

Abstract

The non-commutative five-term relation $T_{1,0} T_{0,1}=T_{0,1} T_{1,1} T_{1,0}$ 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.

Type
Publication
J. Combin. Theory Ser. A 163 (2019), 182–194
Date