# Spherical Stein manifolds and the Weyl involution

Dmitri Akhiezer^{[1]}

- [1] Institute for Information Transmission Problems B. Karetny per. 19 Moscow, 127994 (Russia)

Annales de l’institut Fourier (2009)

- Volume: 59, Issue: 3, page 1029-1041
- ISSN: 0373-0956

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topAkhiezer, Dmitri. "Spherical Stein manifolds and the Weyl involution." Annales de l’institut Fourier 59.3 (2009): 1029-1041. <http://eudml.org/doc/10415>.

@article{Akhiezer2009,

abstract = {We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical subgroups invariant under certain real automorphisms of complex reductive groups.},

affiliation = {Institute for Information Transmission Problems B. Karetny per. 19 Moscow, 127994 (Russia)},

author = {Akhiezer, Dmitri},

journal = {Annales de l’institut Fourier},

keywords = {Reductive groups; spherical subgroups; spherical Stein manifolds; antiholomorphic involutions; reductive groups},

language = {eng},

number = {3},

pages = {1029-1041},

publisher = {Association des Annales de l’institut Fourier},

title = {Spherical Stein manifolds and the Weyl involution},

url = {http://eudml.org/doc/10415},

volume = {59},

year = {2009},

}

TY - JOUR

AU - Akhiezer, Dmitri

TI - Spherical Stein manifolds and the Weyl involution

JO - Annales de l’institut Fourier

PY - 2009

PB - Association des Annales de l’institut Fourier

VL - 59

IS - 3

SP - 1029

EP - 1041

AB - We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical subgroups invariant under certain real automorphisms of complex reductive groups.

LA - eng

KW - Reductive groups; spherical subgroups; spherical Stein manifolds; antiholomorphic involutions; reductive groups

UR - http://eudml.org/doc/10415

ER -

## References

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