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

Abstract

In this paper, we present three families of modular Nahm sums for symmetrizable matrices with arbitrary rank $r\ge 2$ of indices $(2,\dots ,2,1)$ and $(1,\dots ,1,2)$. 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.

59 pages