Monatshefte für Mathematik

, Volume 158, Issue 3, pp 285–305 | Cite as

Segal–Bargmann and Weyl transforms on compact Lie groups



We present an elementary derivation of the reproducing kernel for invariant Fock spaces associated with compact Lie groups which, as Ólafsson and Ørsted showed in (Lie Theory and its Applicaitons in Physics. World Scientific, 1996), yields a simple proof of the unitarity of Hall’s Segal–Bargmann transform for compact Lie groups K. Further, we prove certain Hermite and character expansions for the heat and reproducing kernels on K and \({K_{\mathbb C}}\) . Finally, we introduce a Toeplitz (or Wick) calculus as an attempt to have a quantization of the functions on \({K_{\mathbb C}}\) as operators on the Hilbert space L 2(K).


Segal–Bargmann transform Weyl transform Compact Lie group Hermite functions Reproducing kernel Toeplitz operator 

Mathematics Subject Classification (2000)

22E45 32A25 44A15 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PaderbornPaderbornGermany
  2. 2.Department of MathematicsChalmers University of Technology and Göteborg UniversityGöteborgSweden

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