Non-unitarity of the BKS transformation for symmetric spaces

Abstract

In this paper, we show that the BKS transformation coming from geometric quantization of the cotangent bundle of Riemannian compact symmetric spaces is not always unitary. We will use representation theory of compact Lie groups and Peter–Weyl theory to deduce a simple method to study the unitarity of the transformation. In particular, we show that for S5 this transformation is not unitary. Additionally, we show that in the limit ħ→0 (where ħ is Planck’s constant) asymptotic unitarity holds for all compact symmetric spaces.