Modular Nahm sums for symmetrizable matrices of indices $({2,\ldots, 2},1)$ and $({1,\ldots, 1},2)$

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Julia Q. D. Du, Kathy Q. Ji, Erin Y. Y. Shen, Clara X. Y. Xu
DOI: 10.48550/arxiv.2602.14483
Cited by: 0

Abstract

In this paper, we present three families of modular Nahm sums for symmetrizable matrices with arbitrary rank $r\geq 2$ of indices $({2,\ldots, 2},1)$ and $({1,\ldots, 1},2)$. Specifically, the cases corresponding to $r = 2$ and $r = 3$ of these families have been previously demonstrated by Mizuno, Warnaar, and B. Wang-L. Wang. Building upon these three families, we construct two vector-valued automorphic forms, one of which is a vector-valued modular function when $r$ is odd.

Fields of Study & Subjects

Advanced Mathematical Identities Algebraic structures and combinatorial models Advanced Algebra and Geometry

Publication details

Journal / source
arXiv (Cornell University)
Publication date
16 February 2026
Language
EN
Document type
Preprint