Skew Pieri Rules for Hall-Littlewood Functions

Matjaz Konvalinka, Aaron Lauve

Published 2012-01-06Version 1

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.