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arXiv · 2208.14581

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

Katherine Baker·Shashank Kanade·Matthew C. Russell·Christopher Sadowski
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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 $\mathrm{D}_4^{(3)}$.

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Katherine Baker, Shashank Kanade, Matthew C. Russell, Christopher Sadowski. 2022-08-31. Principal subspaces of basic modules for twisted affine Lie algebras, $q$-series multisums, and Nandi's identities. https://arxiv.org/abs/2208.14581

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