Principal subspaces of basic modules for twisted affine Lie algebras, q-series multisums, and Nandi’s identities
Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1533-1556.

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 integrable, level 4, highest-weight modules of D 4 (3) .

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DOI: 10.5802/alco.311
Classification: 05A15, 05A17, 11P84, 17B69
Keywords: Principal subspaces, vertex operator algebras, affine Lie algebras, Nandi’s identities

Baker, Katherine 1; Kanade, Shashank 2; Russell, Matthew C. 3; Sadowski, Christopher 1

1 Department of Mathematics, Computer Science, and Statistics Ursinus College Collegeville PA 19426
2 Department of Mathematics University of Denver Denver CO 80208
3 Department of Mathematics University of Illinois Urbana-Champaign Urbana IL 61801
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Baker, Katherine; Kanade, Shashank; Russell, Matthew C.; Sadowski, Christopher. Principal subspaces of basic modules for twisted affine Lie algebras, $q$-series multisums, and Nandi’s identities. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1533-1556. doi : 10.5802/alco.311. https://alco.centre-mersenne.org/articles/10.5802/alco.311/

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