Abstract
We consider the standard modules of rectangular highest weights of affine Lie algebras in types and
. By using vertex algebraic techniques we construct the combinatorial bases for standard modules and their principal subspaces and parafermionic spaces. Finally, we compute the corresponding character formulae and, as an application, we obtain two new families of combinatorial identities.
2020 Mathematics Subject Classification:
Acknowledgments
The authors are grateful to Mirko Primc for numerous helpful discussions. The authors would also like to thank Ole Warnaar for bringing to their attention some useful references on combinatorial identities.
Data availability statement
Data sharing not applicable to this article.
Disclosure statement
The authors report there are no competing interests to declare.
Ethical statement
Not applicable to this article.