2020/10/02 by Shashank Kanade, Kanade, Shashank, Matthew C. Russell +1
Mathematics · #11P84 #17B67 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2010.01008
openalex publication_date 2020/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present sum-sides for principal characters of all standard (i.e., integrable and highest-weight) irreducible modules for the affine Lie algebra A2(2). We use modifications of five known Bailey pairs; three of these are sufficient to obtain all the necessary principal characters. We then use the technique of Bailey lattice appropriately extended to include "out-of-bounds" values of one of the parameters, namely, i. We demonstrate how the sum-sides break into six families depending on the level of the modules modulo 6, confirming a conjecture of McLaughlin--Sills.