Classification of smooth affine spherical varieties

By F. Knop, B. V. Steirteghem. 2005

48 citations recorded by the source corpus.

Let G be a complex reductive group. A normal G-variety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form local models for multiplicity free Hamiltonian K-manifolds, K a maximal compact subgroup of G. In this paper, we classify all smooth affine spherical varieties up to coverings, central tori, and ${\mathbb C}^{\times}$-fibrations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/47a9794f636755ec49a59ffe5da46d5bc09e7a08

How researchers see this paper

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In Geometry and Topology

1. N. Perrin
2. Y. Sakellaridis
3. P. Chaput

In Mathematical Physics

1. N. Perrin
2. Y. Sakellaridis

Citations in the corpus

• Spherical varieties and integral representations of L-functions (2009, methodology): “Such an answer has been given in the special case of smooth affine spherical varieties: These varieties automatically have the structure of a preflag bundle, and they have been classified by Knop and Van Steirteghem [2006], and hence can be used to produce Eulerian integrals of automorphic forms! Th”
• ON THE GEOMETRY OF SPHERICAL VARIETIES (2012, background): “Furthermore Knop describes in [93], building on a classification of smooth affine spherical varieties in [94], which moment polytopes and general stabilisers actually occur.”