ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA W(p): A-SERIES

被引：18

作者：

Adamovic, Drazen ^{[1
]}

Lin, Xianzu ^{[2
]}

Milas, Antun ^{[3
]}

机构：

[1] Univ Zagreb, Dept Math, Bijenicka 30, Zagreb 10000, Croatia

[2] Fujian Normal Univ, Coll Math & Comp Sci, Fuzhou 350108, Peoples R China

[3] SUNY Albany, Dept Math & Stat, Albany, NY 12222 USA

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2013年 / 15卷 / 06期

关键词：

Vertex operator algebras; orbifold models; automorphism groups; C-2-cofiniteness; Zhu's algebras; CONFORMAL FIELD-THEORIES; IRREDUCIBLE MODULES; OPERATOR-ALGEBRAS; CLASSIFICATION;

D O I：

10.1142/S0219199713500284

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by [On the triplet vertex algebra W(p), Adv. Math. 217 (2008) 2664-2699], for every finite subgroup Gamma subset of PSL(2, C) we investigate the fixed point subalgebra W(p)(Gamma) of the triplet vertex W(p), of central charge 1 - 6(p-1)(2)/p, p >= 2. This part deals with the A-series in the ADE classification of finite subgroups of PSL(2, C). First, we prove the C-2-cofiniteness of the A(m)-fixed subalgebra W(p)(Am). Then we construct a family of W(p) Am-modules, which are expected to form a complete set of irreducible representations. As a strong support to our conjecture, we prove modular invariance of (generalized) characters of the relevant (logarithmic) modules. Further evidence is provided by calculations in Zhu's algebra for m = 2. We also present a rigorous proof of the fact that the full automorphism group of W(p) is PSL(2, C).

引用

页数：30

共 24 条

[1] Classification of irreducible modules of certain subalgebras of free boson vertex algebra [J].