Quantization in fibering polarizations, Mabuchi rays and geometric Peter-Weyl theorem

sic bound In this paper we use techniques of geometric quantization to give a geometric interpre tation of the Peter Weyl theorem. We present a novel approach to half-form corrected geometric quantization in a specific type of non-K & auml;hler polarizations and study one impor tant class of examples, namely cotangent bundles of compact connected Lie groups K. Our main r refults ults state that this canonically defined polarization occurs in t ary of the space of K K invariant K & auml;hler polarizations equipped with Mabuchi's metric, and that its half-form corrected quantization is isomorphic to the K & auml;hler case. An impor tant rold is played by invariance of the limit polarization under a torus action. Unitary parallel transport the bundle of quantum states along a specific Mabuchi grodesig given by the coherent transform of Hall, relates the non commutative Fourier transform for K with the Borel Weil description of irreducible representations of K. @2024 Elsevier B.V. All rights reserved, including those for and data mining. Al training, and similar technologies.