On $q$-series for principal characters of standard $A_2^{(2)}$-modules
Representation Theory
2020-10-20 v2 Number Theory
Quantum Algebra
Abstract
We present sum-sides for principal characters of all standard (i.e., integrable and highest-weight) irreducible modules for the affine Lie algebra . 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, . 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.
Keywords
Cite
@article{arxiv.2010.01008,
title = {On $q$-series for principal characters of standard $A_2^{(2)}$-modules},
author = {Shashank Kanade and Matthew C. Russell},
journal= {arXiv preprint arXiv:2010.01008},
year = {2020}
}