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Transactions of the American Mathematical Society

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Global character formulae
for compact Lie groups


Authors: A. H. Dooley and N. J. Wildberger
Journal: Trans. Amer. Math. Soc. 351 (1999), 477-495
MSC (1991): Primary 22E30; Secondary 43A75
DOI: https://doi.org/10.1090/S0002-9947-99-02406-X
MathSciNet review: 1638234
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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the concept of a modulator, which leads to a family of character formulae, each generalizing the Kirillov formula. For a suitable choice of modulator, this enables one to understand the Plancherel measure of a compact Lie group as arising from a partition of the identity on the dual of its Lie algebra.


References [Enhancements On Off] (What's this?)

  • 1. N. Berline and M. Vergne, Fourier transforms of orbits of the coadjoint representation, in Representation theory of reductive groups, Birkhäuser, 1983, pp 53-67. MR 85g:22026
  • 2. R. Coifman and G. Weiss, Transference methods in analysis, CBMS lecture notes, Vol. 31, Amer. Math. Soc., Providence, RI, 1977. MR 58:2019
  • 3. A. H. Dooley, J. Repka, and N. J. Wildberger Sums of adjoint orbits, Lin. Multilin. Alg. 36 (1993), 79-101. MR 95k:22025
  • 4. A. H. Dooley and N. J. Wildberger, Harmonic analysis and the global exponential map for compact Lie groups, Funktsional. Anal. i Prilozhen. 27 (1993), no. 1, 25-32; English transl., Funct. Anal. Appl. 27 (1993), 21-27. MR 94e:22032
  • 5. A. H. Dooley and F. Ricci, On the structure of the $G$-invariant Fourier algebra, Boll. Un. Mat. Ital. A (7) 9 (1995), 37-45. MR 96d:43011
  • 6. M. Duflo, Opérateurs différentiels bi-invariants sur un groupe de Lie, Ann. Sci. Ecole Norm. Sup. 10 (1977), 265-288. MR 56:3188
  • 7. F. Ricci and G. Travaglini, $L^p\text{-}L^q$ estimates for orbital measures and Radon transforms on compact Lie groups and Lie algebras, J. Funct. Anal. 129 (1995), 132-147. MR 96c:22016
  • 8. N. R. Wallach, Symplectic geometry and Fourier analysis, Math. Sci. Press, Brookline, MA, 1977. MR 58:7715
  • 9. N. J. Wildberger, Hypergroups and harmonic analysis, Proc. Centre Math. Anal. (ANU) 29 (1992), 238-253. MR 93j:43013

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Additional Information

A. H. Dooley
Affiliation: School of Mathematics, The University of New South Wales, Sydney 2052, Australia

N. J. Wildberger
Affiliation: School of Mathematics, The University of New South Wales, Sydney 2052, Australia

DOI: https://doi.org/10.1090/S0002-9947-99-02406-X
Received by editor(s): April 30, 1995
Article copyright: © Copyright 1999 American Mathematical Society

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