Twisted restricted conformal blocks of vertex operator algebras I: g-twisted correlation functions and fusion rules

被引：0

作者：

Gao, Xu ^{[1
]}

Liu, Jianqi ^{[2
]}

Zhu, Yiyi ^{[3
]}

机构：

[1] Tongji Univ, Dept Math, 1239 Siping Rd, Shanghai 200092, Peoples R China

[2] Univ Penn, Dept Math, 209 South 33rd St, Philadelphia, PA 19104 USA

[3] South China Univ Technol, Dept Math, 381 Wushan Rd, Guangzhou 510641, Guangdong, Peoples R China

来源：

JOURNAL OF ALGEBRA | 2025年 / 675卷

关键词：

Vertex operator algebra; Fusion rule; Twisted module; Conformal block; INTERTWINING-OPERATORS; MODULAR-INVARIANCE; REPRESENTATIONS;

D O I：

10.1016/j.jalgebra.2025.03.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce a notion of g-twisted restricted conformal block on the three-pointed twisted projective line x : C -> P1 associated with an untwisted module M1 and the bottom levels of two g-twisted modules M2 and M3 over a vertex operator algebra V. We show that the space of twisted restricted conformal blocks is isomorphic to the space of gtwisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：59 / 132

页数：74

共 44 条

[1]

Lepowsky J., Calculus of twisted vertex operators, Proc. Natl. Acad. Sci. USA, 82, pp. 8295-8299, (1985)

[2]

Frenkel I., Lepowsky J., Meurman A., Vertex Operator Algebras and the Monster, Pure and Applied Mathematics, 134, (1988)

[3]

Dixon L., Harvey J., Vafa C., Witten E., Strings on orbifolds, Nucl. Phys. B, 261, pp. 678-686, (1985)

[4]

Dijkgraaf R., Vafa C., Verlinde E., Verlinde H., The operator algebra of orbifold models, Commun. Math. Phys., 123, pp. 485-526, (1989)

[5]

Dong C., Lepowsky J., Generalized Vertex Algebras and Relative Vertex Operators, Progress in Mathematics, 112, (1993)

[6]

Xu X., Intertwining operators for twisted modules of a colored vertex operator superalgebra, J. Algebra, 175, pp. 241-273, (1995)

[7]

Dong C., Li H., Mason G., Twisted representations of vertex operator algebras, Math. Ann., 310, pp. 571-600, (1998)

[8]

Dong C., Li H., Mason G., Modular-invariance of trace functions in orbifold theory and generalized Moonshine, Commun. Math. Phys., 214, pp. 1-56, (2000)

[9]

Dong C., Yamskulna G., Vertex operator algebras, generalized doubles and dual pairs, Math. Z., 241, pp. 397-423, (2002)

[10]

Barron K., Dong C., Mason G., Twisted sectors for tensor product vertex operator algebras associated to permutation groups, Commun. Math. Phys., 227, pp. 349-384, (2002)

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