Compact automorphism groups of vertex operator algebras

1996/08/13 by Chongying Dong, Haisheng Li, Dong, Chongying +3 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9608009

latex 9 pages, correct several typos

openalex publication_date 1996/08/13 · arxiv created 1996/08/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for G and the irreducible modules for V^G which are contained in V where V^G is the space of G-invariants of V. We also prove a concomitant Galois correspondence between vertex operator subalgebras of V which contain V^G and closed Lie subgroups of G in the case that G is abelian.

Citations

• Local systems of vertex operators, vertex superalgebras and modules
• Representation theory and tensor product theory for vertex operator algebras

Cited by

• Generalized Symmetries From Fusion Actions
• Symmetry breaking boundaries

Related

• Vertex operator algebras, generalized doubles and dual pairs
• The Automorphism Group of the Vertex Operator Algebra V_L⁺ for an even lattice L without roots
• Quantum Galois theory for compact Lie groups
• The automorphism groups of the vertex operator algebras V_L⁺: general case
• The relationship between skew group algebras and orbifold theory