Five-term relation and Macdonald polynomials

Adriano Garsia, Anton Mellit

Published 2016-04-29Version 1

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.