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

2022/08/31 by Katherine Baker, Baker, Katherine, Shashank Kanade +5 · 1 citation
Mathematics · Physics and Astronomy · #05A15 #05A17 #11P84 #17B69 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2208.14581

openalex publication_date 2022/08/31 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

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 D₄⁽³⁾.

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• On a pair of three-colored (mod 10) partition identities

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