Wednesday, December 11th, 2013
3:00pm - 4:00pm, in McCormack 1-417

Todor Milev

UMass Boston

Subalgebras of finite type of simple Lie algebras

Abstract: A Fernando-Kac subalgebra of a Lie algebra g is a Lie subalgebra which is the subalgebra of locally finitely acting elements for some irreducible representation of g. A Fernando-Kac subalgebra is of finite type if in addition the irreducible module can be chosen to have finite-multiplicity decomposition over the Fernando-Kac subalgebra. We prove that for a fixed semisimple Lie algebra g, up to conjugation, there are only finitely many classes of Fernando-Kac subalgebras of finite type. We then classify the Fernando-Kac subalgebras of finite type in types A_1-A_6, B_2, B_3, C_2-C_5, D_4, and G_2.