Geodesic
Principal subspaces of basic modules for twisted affine Lie algebras, q-series multisums, and Nandi’s identities
Baker, Katherine1 ; Kanade, Shashank2 ; Russell, Matthew C.3 ; Sadowski, Christopher1
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
Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1533-1556

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Baker, Katherine and Kanade, Shashank and Russell, Matthew C. and Sadowski, Christopher},
     title = {Principal subspaces of basic modules for twisted affine {Lie} algebras, $q$-series multisums, and {Nandi{\textquoteright}s} identities},
     journal = {Algebraic Combinatorics},
     pages = {1533--1556},
     publisher = {The Combinatorics Consortium},
     volume = {6},
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     year = {2023},
     doi = {10.5802/alco.311},
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%A Sadowski, Christopher
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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, Tome 6 (2023) no. 6, pp. 1533-1556. doi: 10.5802/alco.311

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