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(2) 2l by Butorac and Sadowski, we construct bases of the highest weight modules of highest weight kΛ 0 and parafermionic spases for the same affine Lie algebras. As a result, we obtain their character formulas conjectured in [14].

Vertex algebraic construction of modules for twisted affine Lie algebras of type $A_{2l}^{(2)}$

“…To obtain a basis of the standard module, we introduce the following lemma. Since relations between twisted vertex operators also holds, the proof is parallel to that of Lemma 5 of [24].…”

“…( (5) b = b and h < h. Note that M QP is upper bounded with respect to this order. By induction in our order " < ", the following proposition is proved in the same way as Proposition 6 in [24] (cf. [4,Lemma 2.3]).…”

“…In [24], we defined the generalized twisted vertex operator for an elements of an extension of the weight lattice P of g to prove the linear independence of B L . In this paper, we continue to use the operator ∆ T c to prove the following theorem.…”

“…In order to do that, we first need to obtain the quasi-particle basis of the principal subspace of the standard module by generalizing the seminal works of Calinescu, Lepowsky, Milas and Penn [6,7] to higher rank and level cases. In the same way as [24], we are able to construct the combinatorial basis of the standard module. In addition to these, we construct the parafermionic basis of the parafermionic space.…”

Generalized Rogers Ramanujan Expressions for Some Non--Singlet Twisted Affine Algebras

“…(2) 2l [9], and for the singlet representation. Our purpose here is to give expressions for some other representations of the twisted affine algebras.…”