Dirac Induction for Loop Groups

Abstract

Using a coset version of the cubic Dirac operators for affine Lie algebras, we give an algebraic construction of the Dirac induction homomorphism for loop group representations. With this, we prove a homogeneous generalization of the Weyl-Kac character formula and show compatibility with Dirac induction for compact Lie groups. © 2010 The Author(s).