An (inverse) Pieri formula for Macdonald polynomials of type C

TL;DR

This paper derives an explicit Pieri formula for Macdonald polynomials of type C and uses it to expand two-row Macdonald polynomials, advancing the understanding of their structure.

Contribution

It introduces a new explicit Pieri formula for type C Macdonald polynomials and provides an inversion method for two-row cases.

Findings

Derived explicit Pieri formula for type C Macdonald polynomials

Obtained explicit expansions for two-row Macdonald polynomials of type C

Enhanced tools for studying Macdonald polynomials in root system C

Abstract

We give an explicit Pieri formula for Macdonald polynomials attached to the root system C_n (with equal multiplicities). By inversion we obtain an explicit expansion for two-row Macdonald polynomials of type C.