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Proceedings of the American Mathematical Society

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Remark on Siegel domains of type $ {\rm III}$

Author: Joseph A. Wolf
Journal: Proc. Amer. Math. Soc. 30 (1971), 487-491
MSC: Primary 32N15; Secondary 53C35
MathSciNet review: 0293125
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Abstract: Bounded symmetric domains have standard realizations as ``Siegel domains of type III.'' Pjateckiĭ-Šapiro has introduced a more restrictive notion of ``Siegel domain of type III.'' Here we give a direct proof that those standard realizations satisfy the additional conditions of the new definition.

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

  • [1] I. I. Pjateckiĭ-Šapiro, Geometry of classical domains and theory of automorphic functions, Fizmatgiz, Moscow, 1961. MR 25 #231.
  • [2] -, Arithmetic groups in complex domains, Uspehi Mat. Nauk 19 (1964), no. 6 (120), 93-121 =Russian Math. Surveys 19 (1964), no. 6, 83-109. MR 32 #7790. MR 0190377 (32:7790)
  • [3] -, Automorphic functions and the geometry of classical domains, Gordon and Breach, New York, 1969. (This is an English translation of [1] incorporating the theory of bounded homogeneous domains.) MR 40 #5908. MR 0252690 (40:5908)
  • [4] J. A. Wolf and A. Korányi, Generalized Cayley transformations of bounded symmetric domains, Amer. J. Math. 87 (1965), 899-939. MR 33 #229. MR 0192002 (33:229)

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