Feigin-Fuchs Duality and Virasoro Vertex Algebras [electronic resource].

9781085683005

Ann Arbor : ProQuest Dissertations & Theses, 2019.

1 online resource (92 p.)

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In this thesis we generalize the Feigin-Fuchs duality for the Verma modules for the Virasoro algebras of central charge 1 and 25 to a correspondence in fusion rules for the representations of the corresponding Virasoro vertex algebras.It is known that the semisimple tensor category generated by ℱ1, the family of irreducible L(1,0) modules which are not isomorphic to Verma modules, is equivalent to the tensor category of finite dimensional irreducible representations of sl(2, ℂ) modified by a 3-cocycle.In chapter 4 we construct an analogous family ℱ25 using Feigin-Fuchs duality and prove that the fusion rules for the L(25,0)-modules in ℱ25 are also in correspondence with the tensor rules for the irreducible finite dimensional representations of sl(2, ℂ). This suggests that the semisimple category generated by the family ℱ25 is also a tensor category equivalent to the semisimple category generated by ℱ1. We conjecture the realization of this equivalence as a bimodule vertex algebra in Chapter 5.

Dissertations & Theses @ Yale University.

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English

January 17, 2020

Thesis (Ph.D.)--Yale University, 2019.

Yale University. Mathematics.