Antiholomorphic involutions of spherical complex spaces
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- by Dmitri Akhiezer and Annett Püttmann PDF
- Proc. Amer. Math. Soc. 136 (2008), 1649-1657 Request permission
Abstract:
Let $X$ be a holomorphically separable irreducible reduced complex space, $K$ a connected compact Lie group acting on $X$ by holomorphic transformations, $\theta : K \to K$ a Weyl involution, and $\mu : X \to X$ an antiholomorphic map satisfying $\mu ^2 =\textrm {Id}$ and $\mu (kx) = \theta (k)\mu (x)$ for $x\in X,\ k\in K$. We show that if ${\mathcal O}(X)$ is a multiplicity free $K$-module, then $\mu$ maps every $K$-orbit onto itself. For a spherical affine homogeneous space $X=G/H$ of the reductive group $G=K^{\mathbb C}$ we construct an antiholomorphic map $\mu$ with these properties.References
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Additional Information
- Dmitri Akhiezer
- Affiliation: Institute for Information Transmission Problems, B. Karetny 19, 101447 Moscow, Russia
- Email: akhiezer@mccme.ru
- Annett Püttmann
- Affiliation: Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätsstraße 150, 44780 Bochum, Germany
- Email: annett.puettmann@rub.de
- Received by editor(s): December 10, 2005
- Received by editor(s) in revised form: November 2, 2006
- Published electronically: January 3, 2008
- Additional Notes: Research was supported by SFB/TR12 “Symmetrien und Universalität in mesoskopischen Systemen” of the Deutsche Forschungsgemeinschaft. The first author was supported in part by the Russian Foundation for Basic Research, Grant 04-01-00647
- Communicated by: Eric Bedford
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1649-1657
- MSC (2000): Primary 32M05; Secondary 43A85
- DOI: https://doi.org/10.1090/S0002-9939-08-08988-0
- MathSciNet review: 2373594