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

作者：Adamovic, Drazen^*; Lin, Xianzu; Milas, Antun

来源：Communications in Contemporary Mathematics, 2013, 15(6): UNSP 1350028.

DOI：10.1142/S0219199713500284

• Vertex operator algebras
• orbifold models
• automorphism groups
• C-2-cofiniteness
• Zhu's algebras

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).

• 出版日期2013-12
• 单位福建师范大学