Symmetry and Pieri rules for the bisymmetric Macdonald polynomials

Bisymmetric Macdonald polynomials can be obtained through a process of antisymmetrization and t-symmetrization of nonsymmetric Macdonald polynomials. Using the double affine Hecke algebra, we show that the evaluation of the bisymmetric Macdonald polynomials satisfies a symmetry property generalizing that satisfied by the usual Macdonald polynomials. We then obtain Pieri rules for the bisymmetric Macdonald polynomials where the sums are over certain vertical strips. (c) 2024 Elsevier Ltd. All rights reserved.