Proof of some Littlewood identities conjectured by Lee, Rains and Warnaar

TL;DR

This paper proves new Littlewood identities for Schur functions, confirming conjectures by Lee, Rains, and Warnaar, and introduces a related identity inspired by Littlewood's classical formulas.

Contribution

It establishes novel Littlewood identities for Schur functions involving partitions with empty 2-core, extending previous conjectures in the Macdonald case.

Findings

Proved conjectured Littlewood identities for Schur functions

Derived a new Littlewood identity inspired by classical formulas

Extended identities to partitions with empty 2-core

Abstract

We prove a novel pair of Littlewood identities for Schur functions, recently conjectured by Lee, Rains and Warnaar in the Macdonald case, in which the sum is over partitions with empty 2-core. As a byproduct we obtain a new Littlewood identity in the spirit of Littlewood's original formulae.