A Classification of the Representations of Reductive Algebraic Groups Which Admit Only a Finite Number of Orbits

DOI10.2307/2374658zbMath0604.20044OpenAlexW2315873232MaRDI QIDQ3741798

Shin-ichi Kasai, Osami Yasukura, Tatsuo Kimura

Publication date: 1986

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374658

zbMATH Keywords

irreducible representationorbitsactionrepresentation of semi-simple algebraic group

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Linear algebraic groups over the reals, the complexes, the quaternions (20G20)

Related Items (8)

Conditions on a finite number of orbits for \(A_r\)-type quivers. ⋮ A classification of 2-simple prehomogeneous vector spaces of type I ⋮ Universal transitivity of reductive prehomogeneous vector spaces with a finite number of orbits ⋮ A classification of a certain class of reductive prehomogeneous vector spaces ⋮ Symmetry in the functional equation of a local zeta distribution ⋮ A characterization of finite prehomogeneous vector spaces associated with products of special linear groups and Dynkin quivers ⋮ A classification of a certain class of reductive prehomogeneous vector spaces. II ⋮ The \(b\)-function and the holonomy diagram of a regular simple prehomogeneous vector space (\(\text{GL}(1)^2 \times\text{Spin} (10)\), half-spin rep. + vector rep.)

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