On actions of a maximal torus on orbits of highest weight vectors

DOI10.1006/jabr.1998.7632zbMath0937.20023OpenAlexW2011835004MaRDI QIDQ1284250

Dmitri I. Panyushev

Publication date: 9 March 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7632

zbMATH Keywords

affine spacespolynomial algebrasirreducible moduleshighest weightsBorel subgroupsmaximal toridominant weightscanonical modulesequidimensional quotient mapssemi-simple simply connected algebraic groups

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Geometric invariant theory (14L24) Group actions on varieties or schemes (quotients) (14L30)

Related Items (4)

Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications ⋮ Actions of ``nilpotent tori on \(G\)-varieties. ⋮ Numerology of square equations ⋮ Weight sum formulae in Lie algebra representations

Cites Work

• Der kanonische Modul eines Invariantenrings. (The canonical module of a ring of invariants)
• On the collapsing of homogeneous bundles
• Cones of highest weight vectors, weight polytopes, and Lusztig's \(q\)-analog
• When is the multiplicity of a weight equal to 1?
• A vanishing theorem for Dolbeault cohomology of homogeneous vector bundles.
• Nef value of homogeneous line bundles and related vanishing theorems
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