An Elliptic Hypergeometric Function Approach to Branching Rules

TL;DR

This paper introduces elliptic hypergeometric functions to prove deformations of classical branching rules, presents new conjectures, and explores unique vanishing behaviors related to partitions with empty 2-cores.

Contribution

It provides the first elliptic hypergeometric integral approach to classical branching rules and proposes novel conjectures involving partitions with special core properties.

Findings

Proved Macdonald-type deformations of classical branching rules.

Identified new vanishing behaviors involving partitions with empty 2-cores.

Proposed conjectural branching rules and related conjectures.

Abstract

We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose some conjectural branching rules and allied conjectures exhibiting a novel type of vanishing behaviour involving partitions with empty 2-cores.