E. B. Vinberg

Weakly symmetric spaces and spherical varieties

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.

A generalized Harish-Chandra isomorphism

Abstract For any complex reductive Lie algebra g and any locally finite g -module V, we extend to the tensor product U ( g ) ⊗ V the Harish-Chandra description of g -invariants in the universal enveloping algebra U ( g ) .

Representations of Finite Groups

In this chapter we are concerned only with finite-dimensional representations, mainly complex ones. Recall that in Section 2 we have shown that every complex linear representation of a finite group is unitary, and hence completely reducible.

An infinitesimal characterization of the complexity of homogeneous spaces

AbstractA characterization of the complexity of a homogeneous space

Real Semisimple Lie Groups

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Lie groups and algebraic groups

of a reductive groupG is given in terms of the mutual position of the tangent Lie algebra of the stabilizer of a generic point of

SEMINAR ON LIE GROUPS AND ALGEBRAIC GROUPS

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