Principal subspaces of basic modules for twisted affine Lie algebras, $q$-series multisums, and Nandi's identities

TL;DR

This paper links $q$-series identities to principal subspaces of twisted affine Lie algebras, introduces new identities including positive and mod 10 identities, and provides novel representations for Nandi's identities.

Contribution

It establishes connections between $q$-series identities and affine Lie algebra modules, and proves two new families of identities with explicit representations.

Findings

Quadruple sum representations for Nandi's identities

A positive representation for the first Nandi identity

New mod 10 identities related to D4^{(3)} modules

Abstract

We provide an observation relating several known and conjectured $q$-series identities to the theory of principal subspaces of basic modules for twisted affine Lie algebras. We also state and prove two new families of $q$-series identities. The first family provides quadruple sum representations for Nandi's identities, including a manifestly positive representation for the first identity. The second is a family of new mod 10 identities connected with principal characters of level 4 integrable, highest-weight modules of $\mathrm{D}_4^{(3)}$.