The Casimir Operator and an application to the multiplication in a G-algebra -- Bart Van Steirteghem, 13 October 2017

We will review the definition of the Casimir Operator of a semisimple lie algebra, and discuss its basic properties. We will then use it to prove a result of Brion's about the multiplication in a G-algebra, i.e. a commutative algebra over the complex numbers with a locally finite action of a complex connected reductive group G by algebra automorphisms.