A Schur-Weyl type duality for twisted weak modules over a vertex algebra

2023/03/28 by K. TANABE, Tanabe, Kenichiro · 1 citation
Mathematics · #17B69 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2303.15692

openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a vertex algebra of countable dimension, G a subgroup of \rm Aut V of finite order, V^G the fixed point subalgebra of V under the action of G, and \mathscr S a finite G-stable set of inequivalent irreducible twisted weak V-modules associated with possibly different automorphisms in G. We show a Schur--Weyl type duality for the actions of \mathscr A_α(G,\mathscr S) and V^G on the direct sum of twisted weak V-modules in \mathscr S where \mathscr A_α(G,\mathscr S) is a finite dimensional semisimple associative algebra associated with G,\mathscr S, and a 2-cocycle α naturally determined by the G-action on \mathscr S. It follows as a natural consequence of the result that for any g∈ G every irreducible g-twisted weak V-module is a completely reducible weak V^G-module.

Cited by

• Y(z)-injective vertex superalgebras and Hopf actions

Related

• Uniform product of A_g,n(V) for an orbifold model V and G-twisted Zhu algebra
• Orbifold theory for vertex algebras and Galois correspondence
• 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
• Vertex operator algebras, generalized doubles and dual pairs
• Twisted representations of vertex operator algebras