Naoki Genra

Last Update 2023/03/31
My research interest is a mathematical study of theories arising from conformal field theory. In particular, I study the algebraic structure and representation theory of Walgebras, which are an important family of vertex algebras in conformal field theory. The Walgebras not only shed new light on the mathematical structure in conformal field theory but also related to affine Lie algebras, modular tensor categories, and quantum geometric Langlands programs so that Walgebras will play an important role to connect various representation theories with each other. My main tool to study Walgebras is screening operators, which give rise to new realizations of Walgebras and is useful to prove nontrivial isomorphisms between Walgebras. In fact, I have recently applied screening operators to prove FeiginSemikhatov conjectures (dualities between Walgebras) and to study the representation theory of the Walgebras. I also research the relationship between screening operators and geometric realizations of Walgebras.
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