Partially-Symmetric Macdonald Polynomials

TR Number
Date
2022-03-29
Journal Title
Journal ISSN
Volume Title
Publisher
Virginia Tech
Abstract

Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald polynomials interpolate between the symmetric and nonsymmetric types. We begin developing theory for these partially-symmetric polynomials, and prove results including their stability, an integral form, and a Pieri-like formula for their multiplication with certain elementary symmetric functions.

Description
Keywords
Macdonald theory, Partially Symmetric, Almost Symmetric
Citation