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Weakly symmetric spaces and spherical varieties (1999)

Akhiezer, D. N. ; Vinberg, E. B.

Springer

Transformation groups 4 (1999), S. 3-24

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ISSN: 1531-586X

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Weakly symmetric homogeneous spaces were introduced by A. Selberg in 1956. We prove that, for a real reductive algebraic group, they can be characterized as the spaces of real points of affine spherical homogeneous varieties of the complexified group. As an application, under the same assumption on the transitive group, we show that weakly symmetric spaces are precisely the homogeneous Riemannian manifolds with commutative algebra of invariant differential operators.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01236659

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