The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2

2019/10/16 by Tanabe, Kenichiro
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1910.07126

Abstract

Let V_L be the vertex algebra associated to a non-degenerate even lattice L, θ the automorphism of V_L induced from the -1 symmetry of L, and V_L⁺ the fixed point subalgebra of V_L under the action of θ. We classify the irreducible weak V_L⁺-modules and show that any irreducible weak V_L⁺-module is isomorphic to a weak submodule of some irreducible weak V_L-module or to a submodule of some irreducible θ-twisted V_L-module.

Related

• The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 2)
• Representations of the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2
• Classification of irreducible modules of the vertex algebra V_L⁺ when L is a nondegenerate even lattice of an arbitrary rank
• Classification of irreducible modules for the vertex operator algebra V_L⁺: General case
• Rationality of the vertex operator algebra V_L⁺ for a positive definite even lattice L