The Capelli identity and unitary representations

Siddhartha Sahi

Compositio Mathematica (1992)

  • Volume: 81, Issue: 3, page 247-260
  • ISSN: 0010-437X

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Sahi, Siddhartha. "The Capelli identity and unitary representations." Compositio Mathematica 81.3 (1992): 247-260. <http://eudml.org/doc/90139>.

@article{Sahi1992,
author = {Sahi, Siddhartha},
journal = {Compositio Mathematica},
keywords = {irreducible Hermitian symmetric space; Jordan norm; Lie algebra; induced representation; invariant Hermitian form; Hermitian pairing},
language = {eng},
number = {3},
pages = {247-260},
publisher = {Kluwer Academic Publishers},
title = {The Capelli identity and unitary representations},
url = {http://eudml.org/doc/90139},
volume = {81},
year = {1992},
}

TY - JOUR
AU - Sahi, Siddhartha
TI - The Capelli identity and unitary representations
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 81
IS - 3
SP - 247
EP - 260
LA - eng
KW - irreducible Hermitian symmetric space; Jordan norm; Lie algebra; induced representation; invariant Hermitian form; Hermitian pairing
UR - http://eudml.org/doc/90139
ER -

References

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  5. [KaV] M. Kashiwara and M. Vergne, Functions on the Shilov Boundary of the Generalized Half Plane, Non-Commutative Harmonic Analysis, Lect. Notes Math. 728, Springer, 1979, pp. 136-176. Zbl0416.22006MR548329
  6. [KorW] A. Koranyi and J. Wolf, Realization of Hermitian Symmetric Spaces as Generalized Halfplanes, Ann. of Math.81 (1965), 265-268. Zbl0137.27402MR174787
  7. [KosR] B. Kostant and S. Rallis, Orbits and Representations Associated to Symmetric Spaces, Amer. J. Math.93 (1971), 753-809. Zbl0224.22013MR311837
  8. [KosS] B. Kostant and S. Sahi, The Capelli Identity, Tube Domains and the Generalized Laplace Transform, Adv. Math.87 (1991), 71-92. Zbl0748.22008MR1102965
  9. [KuR] S. Kudla and S. Rallis, Degenerate Principal Series and Invariant Distributions, Israel J. Math.69 (1990), 25-45. Zbl0708.22005MR1046171
  10. [M] C. Moore, Compactifications of Symmetric Domains II. The Cartant Domains, Amer. J. Math.86 (1964), 358-378. Zbl0156.03202MR161943
  11. [RV] H. Rossi and M. Vergne, Analytic Continuation of the Holomorphic Discrete Series of a Semi-simple Lie Group, Acta Math. 136 (1976), 1-59. Zbl0356.32020MR480883
  12. [S] B. Speh, Degenerate Series Representations of the Universal Covering Group of SU(2, 2), J. Funct. Anal.33 (1979), 95-118. Zbl0415.22012MR545386
  13. [VZ] D. Vogan and G. Zuckerman, Unitary Representations with Non-Zero Cohomology, Comp. Math.53 (1984), 51-90. Zbl0692.22008MR762307
  14. [W] N. Wallach, The Analytic Continuation of the Discrete Series II, Trans. Amer. Math. Soc.251 (1979), 19-37. Zbl0419.22018MR531967

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