Tricritical 3-State Potts Model and Vertex Operator Algebras Constructed from Ternary Codes

Abstract

We construct a class of vertex operator algebras based on the tricritical 3-state Potts model L(6/7, 0) and some ternary codes. We also compute their irreducible modules. In addition, we show that there is a natural VOA automorphism of order 3 or 1 associated with a subalgebra isomorphic to L(6/7, 0) ⊕ L(6/7, 5).

Key Words:

• Vertex operator algebra
• Virasoro algebra
• Conformal vectors
• Ternary codes

Mathematics Subject Classification:

• 17B68
• 17B69

Acknowledgments

The first author is partially supported by NSC grant 90-2115-M-006-027 of Taiwan, R.O.C. The second author is partially supported by JSPS Grant-in-Aid for Scientific Research No. 13640012.

Notes

^#Communicated by K. Misra.