Dirac induction for loop groups (Q621819)

The author gives a simple algebraic construction of Dirac induction for loop groups. This construction induces finite dimensional representations of a compact Lie group \(H\) to positive energy representations of the loop group \(LG\), where \(H\subset G\) is an equal rank embedding. The main tool of the construction is a homogeneous generalization of the representation theoretic cubic Dirac operator. As an application, the author proves a homogeneous generalization of the Weyl-Kac character formula. The results of the paper are heavily influenced by the results of \textit{G. D. Landweber} [Duke Math. J. 110, No.~1, 121--160 (2001; Zbl 1018.17016)].