Principal subspaces of basic modules for twisted affine Lie algebras, $q$-series multisums, and Nandi's identities
- Resource Type
- Working Paper
- Authors
- Baker, Katherine; Kanade, Shashank; Russell, Matthew C.; Sadowski, Christopher
- Source
- Subject
- Mathematics - Combinatorics
Mathematics - Number Theory
Mathematics - Quantum Algebra
Mathematics - Representation Theory
05A15, 05A17, 11P84, 17B69
- Language
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 $\mathrm{D}_4^{(3)}$.
Comment: See ancillary files for Maple programs regarding proof verification