The A_2n⁽²⁾ Rogers-Ramanujan identities

2013/09/20 by S. Ole Warnaar, Warnaar, S. Ole · 1 citation
Mathematics · #05E05 #05E10 #11P84 #17B67 #33D67 #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1309.5216

openalex publication_date 2013/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The famous Rogers-Ramanujan and Andrews--Gordon identities are embedded in a doubly-infinite family of Rogers-Ramanujan-type identities labelled by positive integers m and n. For fixed m and n the product side corresponds to a specialised character of the affine Kac-Moody algebra A_2n⁽²⁾ at level m, and is expressed as a product of n² theta functions of modulus 2m+2n+1, or by level-rank duality, as a product of m² theta functions. Rogers-Ramanujan-type identities for even moduli, corresponding to the affine Lie algebras C_n⁽¹⁾ and D_n+1⁽²⁾, are also proven.

Cited by

• Leading terms of relations for standard modules of affine Lie algebras C_n\sp(1)

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