Japanese Journal of Mathematics

, Volume 3, Issue 2, pp 247–290

Covariant quantization: spectral analysis versus deformation theory


DOI: 10.1007/s11537-008-0831-7

Cite this article as:
Pevzner, M. Jpn. J. Math. (2008) 3: 247. doi:10.1007/s11537-008-0831-7


Formal deformation or rather symbolic calculus? To which extent do these approaches complete each other in the study of symmetry-preserving quantization procedures for homogeneous spaces? The representation theory of underlying Lie groups shows that the answer is much more delicate than initially thought and that it cannot be always reduced to asymptotic expansions with respect to some Planck’s constant. The main goal of this survey is to give hints regarding the aims of each approach and, on the domain where these intersect, to compare the answers they lead to.

Keywords and phrases:

quantization unitary representations semisimple symmetric spaces 

Mathematics Subject Classification (2000):

81-02 22E46 43A85 47G30 16S80 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2008

Authors and Affiliations

  1. 1.FRE 3111 du CNRSUniversité de ReimsReimsFrance

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