Title: Invariants in enveloping algebras and vacuum modules
Speaker: Alexander Molev (Sydney University)
Abstract: Given a simple Lie algebra g and its Cartan subalgebra h, the Chevalley theorem provides an isomorphism between the algebra of g-invariants of the symmetric algebra S(g) and the algebra of invariants in S(h) under the action of the Weyl group. The Harish-Chandra theorem gives a noncommutative (or quantum) version of this isomorphism by describing the center of the universal enveloping algebra U(g). We will discuss how these theorems are generalized to an affine setting, where g is replaced with the corresponding affine Kac-Moody algebra. The vacuum modules and their invariants will play a key role in this generalization.