Functions on the universal cover of the principal nilpotent orbit

DOI10.1007/BF02100596zbMath0781.22010OpenAlexW1964359544MaRDI QIDQ1207418

William A. Graham

Publication date: 1 April 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143985

zbMATH Keywords

Lie algebrahighest weightadjoint representationmaximal torusregular functionsdominant weightsaugmentation idealcomplex simply connected semisimple Lie groupequivariant gradingprincipal nilpotent orbit

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Cohomology theory for linear algebraic groups (20G10) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

On Lusztig’s q-Analogues of All Weight Multiplicities of a Representation, On the equivariant 𝐾-theory of the nilpotent cone, Irreducible Local Systems on Nilpotent Orbits, Generic singularities of nilpotent orbit closures, Invariant Hilbert scheme of the Cox realization of the nilpotent cone in \(\mathfrak{sl}(n)\), Unnamed Item, Actions of ``nilpotent tori on \(G\)-varieties., Unnamed Item, Complex adjoint orbits in Lie theory and geometry, Line bundles on the cotangent bundle of the flag variety

Cites Work

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• Cohomology of induced representations for algebraic groups
• Rings of regular functions on nilpotent orbits and their covers
• The normality of closures of orbits in a Lie algebra
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• Limits of Weight Spaces, Lusztig's q-Analogs, and Fiberings of Adjoint Orbits
• Nilpotent orbits, normality,\\ and Hamiltonian group actions
• Lie Group Representations on Polynomial Rings
• Introduction to Lie Algebras and Representation Theory