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Lie Group Quantum Mathematics Seminar

New perspectives on fixed point subalgebras of affine Lie algebras corresponding to Dynkin diagram automorphisms

Terence Coelho, Rutgers University

Location:  Hill 705
Date & time: Wednesday, 20 March 2024 at 11:45AM - 12:45PM

We present new realizations of the simply-laced affine Lie algebras that do not distinguish any node in the affine Dynkin diagram, which allows one to more easily study the fixed-point subalgebras corresponding to affine Dynkin diagram automorphisms. We show how these fixed-point subalgebras compare to the associated non-simply-laced affine Lie algebras, and present an alternative classification of affine root systems and affine Lie algebras from this perspective. Finally, we discuss the corresponding realizations of the level-one irreducible highest weight modules for a simply-laced affine Lie algebra and how the affine Dynkin diagram automorphisms can be lifted to their direct sum.

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