3.30 pm, Lecture Hall 6
Classification of regular subalgebras of affine Lie algebras
R. Venkatesh
IISc Bangalore.
23-01-19

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Abstract

E. B. Dynkin introduced the notion of regular semi-simple subalgebras (regular subalgebras) in order to classify all the semi-simple subalgebras of finite-dimensional complex semi-simple Lie algebras. The classification of regular subalgebras is carried out in terms of their root systems, which are closed subroot systems of the root system of the ambient Lie algebra. One can naturally generalize the notion of regular subalgebras to affine Kac-Moody algebras or more generally to any Kac-Moody algebras. In this talk, I will explain how one reduces the problem of classification of regular subalgebras of affine Kac-Moody algebras to the classification of maximal closed subroot systems of real affine root systems which can be described very explicitly in terms their gradient root systems (finite part) and some compatible cosets of integers. This is joint work with Krishanu Roy.