Parafermionic Bases of Standard Modules for Twisted Affine Lie Algebras of Type $A_{2l-1}^{(2)}$, $D_{l+1}^{(2)}$, $E_{6}^{(2)}$ and $D_{4}^{(3)}$

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 kΛ0 and parafermionic spases for the same affine Lie algebras. As a result, we obtain their character formulas conjectured in Hatayama et al. (2001).