Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Antiholomorphic involutions of spherical complex spaces

Authors: Dmitri Akhiezer and Annett Püttmann
Journal: Proc. Amer. Math. Soc. 136 (2008), 1649-1657
MSC (2000): Primary 32M05; Secondary 43A85
Published electronically: January 3, 2008
MathSciNet review: 2373594
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 ={\rm 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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32M05, 43A85

Retrieve articles in all journals with MSC (2000): 32M05, 43A85

Additional Information

Dmitri Akhiezer
Affiliation: Institute for Information Transmission Problems, B. Karetny 19, 101447 Moscow, Russia

Annett Püttmann
Affiliation: Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätsstraße 150, 44780 Bochum, Germany

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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society