Factorizations of symmetric Macdonald polynomials

Abstract

We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. As a consequence we prove a conjecture of Bernevig and Haldane stated in the context of the fractional quantum Hall theory.

Dédicacé à Jean-Yves Thibon pour son soixantième anniversaire. 34 pages, 4 figures