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Lie Groups Quantum Mathematics Seminar

 Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras

 Sven Moeller, Rutgers University

Location:  HILL 705
Date & time: Friday, 15 September 2017 at 12:00PM - 1:00PM

Abstract :  We prove a dimension formula for orbifold vertex operator algebras of central charge 24 by automorphisms of order \(n\) such that \(Gamma_0(n)\) is a genus zero group. We then use this formula together with the inverse orbifold construction for automorphisms of orders 2, 4, 5, 6 and 8 to establish that each of the following fifteen Lie algebras is the weight-one space \(V_1\) of exactly one holomorphic, \(C_2\)-cofinite vertex operator algebra \(V\) of CFT-type of central charge 24: \(A_5C_5E_{6,2}\), \(A_3A_{7,2}C_3^2\), \(A_{8,2}F_{4,2}\), \(B_8E_{8,2}\), \(A_2^2A_{5,2}^2B_2\), \(C_8F_4^2\), \(A_{4,2}^2C_{4,2}\), \(A_{2,2}^4D_{4,4}\), \(B_5E_{7,2}F_4\), \(B_4C_6^2\), \(A_{4,5}^2\), \(A_4A_{9,2}B_3\), \(B_6C_{10}\), \(A_1C_{5,3}G_{2,2}\) and \(A_{1,2}A_{3,4}^3\).

This is joint work with Nils Scheithauer (Darmstadt) and Jethro van Ekeren (IMPA, Rio de Janeiro).

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