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ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA : A-SERIES

DRAŽEN ADAMOVIĆ

Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia

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XIANZU LIN

College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350108, P. R. China

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, and

ANTUN MILAS

Department of Mathematics and Statistics, SUNY-Albany, 1400 Washington Avenue, Albany, NY 12222, USA

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https://doi.org/10.1142/S0219199713500284Cited by:18 (Source: Crossref)

Abstract

Motivated by [On the triplet vertex algebra , Adv. Math.217 (2008) 2664–2699], for every finite subgroup Γ ⊂ PSL(2, ℂ) we investigate the fixed point subalgebra of the triplet vertex , of central charge , p ≥ 2. This part deals with the A-series in the ADE classification of finite subgroups of PSL(2, ℂ). First, we prove the C₂-cofiniteness of the A_m-fixed subalgebra . Then we construct a family of -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 is PSL(2, ℂ).

Keywords:

AMSC: 17B69, 17B68

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