Generalized Andrews-Gordon Identities

2015/06/16 by Hannah Larson, Larson, Hannah
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1506.05063

openalex publication_date 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper, Griffin, Ono and Warnaar present a framework for Rogers-Ramanujan type identities using Hall-Littlewood polynomials to arrive at expressions of the form ∑_{λ: λ1 ≤ m} q^a|λ|P_2λ(1,q,q²,… ; qⁿ) = "Infinite product modular function" for a = 1,2 and any positive integers m and n. A recent paper of Rains and Warnaar presents further Rogers-Ramanujan type identities involving sums of terms q^|λ|/2P_λ(1,q,q²,…;qⁿ). It is natural to attempt to reformulate these various identities to match the well-known Andrews-Gordon identities they generalize. Here, we find combinatorial formulas to replace the Hall-Littlewood polynomials and arrive at such expressions.

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• A generalization of Kawanaka's identity for Hall-Littlewood polynomials and applications
• The Rogers-Ramanujan Identities, the Finite General Linear Groups, and the Hall-Littlewood Polynomials
• A motivated proof of Gordon's identities
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