Polynomiality of invariants, unimodularity and adapted pairs

DOI10.1007/s00031-010-9113-6zbMath1275.17022OpenAlexW2003318826MaRDI QIDQ626577

Anthony Joseph, Doron Shafrir

Publication date: 18 February 2011

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00031-010-9113-6

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Actions of groups on commutative rings; invariant theory (13A50) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (26)

Jordan-Kronecker invariants of finite-dimensional Lie algebras ⋮ Weierstrass sections for some truncated parabolic subalgebras ⋮ On Dixmier's fourth problem ⋮ Some remarks about Mishchenko-Fomenko subalgebras ⋮ A generalization of Veldkamp's theorem for a class of Lie algebras ⋮ Takiff algebras with polynomial rings of symmetric invariants ⋮ On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebras ⋮ On the semi-centre of a Poisson algebra ⋮ The maximal abelian dimension of a Lie algebra, Rentschler's property and Milovanov's conjecture ⋮ The hidden semi-invariants generators of an almost-Frobenius biparabolic ⋮ Weierstrass sections for parabolic adjoint action in type \(A\) ⋮ Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials ⋮ The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven ⋮ Slices for biparabolics of index 1 ⋮ Slices for maximal parabolic subalgebras of a semisimple Lie algebra ⋮ The symmetric invariants of centralizers and Slodowy grading. II ⋮ The symmetric invariants of centralizers and Slodowy grading ⋮ One-parameter contractions of Lie-Poisson brackets ⋮ Unnamed Item ⋮ About Polynomiality of the Poisson Semicentre for Parabolic Subalgebras ⋮ Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants ⋮ The integrality of an adapted pair ⋮ The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem ⋮ Polynomiality for the Poisson centre of truncated maximal parabolic subalgebras ⋮ An algebraic slice in the coadjoint space of the Borel and the Coxeter element ⋮ Adapted pairs in type A and regular nilpotent elements

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Remarks on real nilpotent orbits of a symmetric pair
• Clifford algebra analogue of the Hopf-Koszul-Samelson theorem, the \(\rho\)-decomposition \(C({\mathfrak g})=\text{End }V_ \rho\otimes C(P)\), and the \({\mathfrak g}\)-module structure of \(\bigwedge {\mathfrak g}\)
• Slices for biparabolic coadjoint actions in type A
• The argument shift method and maximal commutative subalgebras of Poisson algebras
• Computing invariants and semi-invariants by means of Frobenius Lie algebras
• Compatible adapted pairs and a common slice theorem for some centralizers
• On the semi-center of a universal enveloping algebra
• Commutative families of functions related to consistent Poisson brackets
• A preparation theorem for the prime spectrum of a semisimple Lie algebra
• A degree inequality for Lie algebras with a regular Poisson semi-center
• On the coadjoint representation of \(\mathbb Z_2\)-contractions of reductive Lie algebras
• On semi-invariants and index for biparabolic (seaweed) algebras. II.
• On symmetric invariants of centralisers in reductive Lie algebras
• Parabolic actions in type \(A\) and their eigenslices
• Maximal Poisson commutative subalgebras for truncated parabolic subalgebras of maximal index in \(\mathfrak{sl}_n\)
• The sum of the false degrees -- a mystery in the theory of invariants
• A note on the parametrization of conjugacy classes
• Stone Duality for Nominal Boolean Algebras with И
• Computing with Nilpotent Orbits in Simple Lie Algebras of Exceptional Type
• INVARIANTS OF FINITE GROUP SCHEMES
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES
• Lie Group Representations on Polynomial Rings
• A counterexample to Premet's and Joseph's conjectures
• Semi-centre de l'algèbre enveloppante d'une sous-algèbre parabolique d'une algèbre de Lie semi-simple☆

This page was built for publication: Polynomiality of invariants, unimodularity and adapted pairs