Signature quantization

Abstract

We associate to the action of a compact Lie group G on a line bundle over a compact oriented even-dimensional manifold a virtual representation of G using a twisted version of the signature operator. We obtain analogues of various theorems in the more standard theory of geometric quantization. Some of these results were announced in Guillemin, Sternberg and Weitsman, 2003. © 2003 Applied Probability Trust.