Bailey Pairs and an Identity of Chern-Li-Stanton-Xue-Yee

TL;DR

The paper develops a streamlined Bailey-pair framework to prove the identity of Chern–Li–Stanton–Xue–Yee and to generate a broad class of related $q$-series identities. By combining the classical Bailey lemma, the Bailey lattice, and targeted seed sequences $f_n$, it reduces complex $q$-multisums to theta-type products, producing theta and false theta families, including a detailed proof of the CLSXY identity. A dilation theorem extends the method to new families and explicit product-difference formulas, linking dilated multisums to known product identities. Together, these results illustrate the power of Bailey-pairs in organizing and deriving $q$-series identities with rich combinatorial and representation-theoretic structure, and they place the CLSXY identity within a broad, systematic framework.

Abstract

We show how Bailey pairs can be used to give a simple proof of an identity of Chern, Li, Stanton, Xue, and Yee. The same method yields a number of related identities as well as false theta companions.

Theorems & Definitions (29)

• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Theorem 1.4
• Theorem 1.5
• Theorem 1.6
• Lemma 2.1: Andmultiple
• Lemma 2.2: AABLattice
• Lemma 2.3: Lo1
• Lemma 2.4: Lo0