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

Author:

Tanabe Kenichiro

Abstract

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

Funder

Japan Society for the Promotion of Science

Publisher

American Mathematical Society (AMS)

Reference26 articles.

1. Rationality, regularity, and 𝐶₂-cofiniteness;Abe, Toshiyuki;Trans. Amer. Math. Soc.,2004

2. On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras;Adamović, Dražen;J. Algebra,2019

3. D. Adamović, C. H. Lam, V. Pedić, and N. Yu, \textsl{On irreducibility of modules of Whittaker type: twisted modules and nonabelian orbifolds}, arXiv:2212.14137, 2022.

4. Vertex algebras, Kac-Moody algebras, and the Monster;Borcherds, Richard E.;Proc. Nat. Acad. Sci. U.S.A.,1986

5. The operator algebra of orbifold models;Dijkgraaf, Robbert;Comm. Math. Phys.,1989

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3