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Z3 symmetry and W3 algebra in lattice vertex operator algebras

Chongying Dong & Ching Hung Lam & Kenichiro Tanabe & Hiromichi Yamada & Kazuhiro Yokoyama

Abstract

The W3 algebra of central charge 6 ∕ 5 is realized as a subalgebra of the vertex operator algebra V √- 2A2 associated with a lattice of type √2A2 by using both coset construction and orbifold theory. It is proved that W3 is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.
Authors
Chongying Dong
Department of Mathematics
University of California
Santa Cruz, CA 95064
Ching Hung Lam
Department of Mathematics
National Cheng Kung University
Tainan, Taiwan 701
Republic of China
Kenichiro Tanabe
Institute of Mathematics
University of Tsukuba
Tsukuba 305-8571
Japan
Hiromichi Yamada
Department of Mathematics
Hitotsubashi University
Kunitachi, Tokyo 186-8601
Japan
Kazuhiro Yokoyama
Graduate School of Mathematics
Kyushu University
Fukuoka 812-8581
Japan