Combinatorial bases of standard modules of twisted affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$: rectangular highest weights

TL;DR

This paper constructs combinatorial bases for standard modules of certain twisted affine Lie algebras using vertex algebra techniques, leading to new character formulas and combinatorial identities.

Contribution

It introduces explicit combinatorial bases for modules of twisted affine Lie algebras of types A and D, and derives new character formulas and identities.

Findings

Constructed combinatorial bases for standard modules and principal subspaces.

Derived explicit character formulas for these modules.

Produced two new families of combinatorial identities.

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.