Parafermionic bases of standard modules for twisted affine Lie algebras of type $A_{2l-1}^{(2)}$, $D_{l+1}^{(2)}$, $E_6^{(2)}$ and $D_4^{(3)}$

TL;DR

This paper constructs bases for highest weight modules and parafermionic spaces of certain twisted affine Lie algebras, confirming conjectured character formulas and extending previous work on principal subspaces.

Contribution

It introduces new bases for modules of twisted affine Lie algebras and proves their character formulas, advancing the understanding of their structure.

Findings

Constructed bases for modules of specific twisted affine Lie algebras.

Derived and confirmed character formulas for these modules.

Extended previous principal subspace results to new algebra types.

Abstract

Using the bases of principal subspaces for twisted affine Lie algebras except $A_{2l}^{(2)}$ by Butorac and Sadowski, we construct bases of the highest weight modules of highest weight $k\Lambda_0$ and parafermionic spases for the same affine Lie algebras. As a result, we obtain their character formulas conjectured in arXiv:math/0102113.