Combinatorial bases of standard modules of twisted affine Lie algebras in types and : rectangular highest weights

Abstract

We consider the standard modules of rectangular highest weights of affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. 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.

Keywords:

• Combinatorial basis
• parafermionic space
• principal subspace
• standard module

2020 Mathematics Subject Classification:

• Primary: 17B67
• Secondary: 17B69, 05A19

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.

Additional information

Funding

This work has been supported in part by Croatian Science Foundation under the project UIP-2019-04-8488. The first author is partially supported by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004).