Quantization on compact lie groups

Veronique Fischer, Michael Ruzhansky

Research output: Chapter in Book/Report/Conference proceedingChapter

16 Citations (Scopus)

Abstract

In this chapter we briefly review the global quantization of operators and symbols on compact Lie groups following [RT13] and [RT10a] as well as more recent developments of this subject in this direction. Especially the monograph [RT10a] can serve as a companion for the material presented here, so we limit ourselves to explaining the main ideas only. This quantization yields full (finite dimensional) matrix-valued symbols for operators due to the fact that the unitary irreducible representations of compact Lie groups are all finite dimensional. Here, in order to motivate the developments on nilpotent groups, which is the main subject of the present monograph, we briefly review key elements of this theory referring to [RT10a] or to other sources for proofs and further details.

Original languageEnglish
Title of host publicationQuantization on Nilpotent Lie Groups
PublisherBirkhäuser
Pages57-90
Number of pages34
ISBN (Print)9783319295572
DOIs
Publication statusPublished - Mar 2016

Publication series

NameProgress in Mathematics
Volume314

Fingerprint

Compact Lie Group
Quantization
Nilpotent Group
Operator
Irreducible Representation
Review

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Fischer, V., & Ruzhansky, M. (2016). Quantization on compact lie groups. In Quantization on Nilpotent Lie Groups (pp. 57-90). (Progress in Mathematics; Vol. 314). Birkhäuser. https://doi.org/10.1007/978-3-319-29558-9_2

Quantization on compact lie groups. / Fischer, Veronique; Ruzhansky, Michael.

Quantization on Nilpotent Lie Groups. Birkhäuser, 2016. p. 57-90 (Progress in Mathematics; Vol. 314).

Research output: Chapter in Book/Report/Conference proceedingChapter

Fischer, V & Ruzhansky, M 2016, Quantization on compact lie groups. in Quantization on Nilpotent Lie Groups. Progress in Mathematics, vol. 314, Birkhäuser, pp. 57-90. https://doi.org/10.1007/978-3-319-29558-9_2
Fischer V, Ruzhansky M. Quantization on compact lie groups. In Quantization on Nilpotent Lie Groups. Birkhäuser. 2016. p. 57-90. (Progress in Mathematics). https://doi.org/10.1007/978-3-319-29558-9_2
Fischer, Veronique ; Ruzhansky, Michael. / Quantization on compact lie groups. Quantization on Nilpotent Lie Groups. Birkhäuser, 2016. pp. 57-90 (Progress in Mathematics).
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