X-Nico

Geometric invariant theory

E.B. Vinberg, V.L. Popov, Invariant theory, in Algebraic geometry.

Prehomogeneous vector space

E. B. Vinberg, On the classification of the nilpotent elements of graded Lie algebras, Soviet Math Doklady, volume 16 (1975) 1517-1520.

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This shows in particular (and was noted independently by Vinberg in 1975) that the Levi factor G of P acts prehomogeneously on $V:=\backslash mathfrak\; p^\backslash perp/\backslash mathfrak\; p^\backslash perp,\backslash mathfrak\; p^\backslash perp$.

Symmetric space

(Selberg's assumption that s² should be an element of G was later shown to be unnecessary by Ernest Vinberg.)

see also