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


Author: Joseph A. Wolf
Journal: Proc. Amer. Math. Soc. 30 (1971), 487-491
MSC: Primary 32N15; Secondary 53C35
DOI: https://doi.org/10.1090/S0002-9939-1971-0293125-7
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?)

    I. I. Pjateckiĭ-Šapiro, Geometry of classical domains and theory of automorphic functions, Fizmatgiz, Moscow, 1961. MR 25 #231.
  • I. I. Pjateckiĭ-Šapiro, Arithmetic groups in complex domains, Uspehi Mat. Nauk 19 (1964), no. 6 (120), 93–121 (Russian). MR 0190377
  • I. I. Pyateskii-Shapiro, Automorphic functions and the geometry of classical domains, Mathematics and its Applications, Vol. 8, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Translated from the Russian. MR 0252690
  • Joseph A. Wolf and Adam Korányi, Generalized Cayley transformations of bounded symmetric domains, Amer. J. Math. 87 (1965), 899–939. MR 192002, DOI https://doi.org/10.2307/2373253

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Article copyright: © Copyright 1971 American Mathematical Society