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

Abstract

Let g be the affine Lie algebra of type A(2) 2l . The integrable highest weight g-module L(kΛ 0 ) called the standard g-module is realized by a tensor product of the twisted module V T L for the lattice vertex operator algebra V L . By using such vertex algebraic construction, we construct bases of the standard module, its principal subspace and the parafermionic space. As a consequence, we obtain their character formulas and settle the conjecture for vacuum modules stated in [15].