Skew Pieri Rules for Hall-Littlewood Functions

TL;DR

This paper establishes skew Pieri rules for Hall-Littlewood functions, using q-binomial identities and Hopf algebra techniques, confirming conjectures and expanding the algebraic understanding of these functions.

Contribution

It proves skew Pieri rules for Hall-Littlewood functions, including conjectured cases, via novel q-binomial and Hopf algebra identities.

Findings

Proved skew Pieri rules for Hall-Littlewood functions

Confirmed conjectures by the first author

Developed new algebraic identities involving q-binomial coefficients

Abstract

We produce skew Pieri Rules for Hall--Littlewood functions in the spirit of Assaf and McNamara. The first two were conjectured by the first author. The key ingredients in the proofs are a q-binomial identity for skew partitions and a Hopf algebraic identity that expands products of skew elements in terms of the coproduct and the antipode.