Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups

DOI10.1007/s10468-010-9207-9zbMath1250.13005arXiv0809.3558OpenAlexW1989982724MaRDI QIDQ434430

Akihito Wachi, Toshiaki Maeno, Yasuhide Numata

Publication date: 10 July 2012

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.3558

zbMATH Keywords

Coxeter GroupFlag VarietyLefschetz Propertyring of co-invariantsWeyl Group

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15) Actions of groups on commutative rings; invariant theory (13A50) Classical problems, Schubert calculus (14N15)

Related Items (10)

Lefschetz properties and hyperplane arrangements ⋮ Vandermondes in superspace ⋮ Vandermondes, superspace, and delta conjecture modules ⋮ Gelfand-Tsetlin theory for rational Galois algebras ⋮ The Lefschetz elements of coinvariant algebras of binary polyhedral groups. ⋮ The Hodge theory of Soergel bimodules. ⋮ The strong Lefschetz property of the coinvariant ring of the Coxeter group of type \(H_{4}\) ⋮ Power sum decompositions of defining equations of reflection arrangements ⋮ Lefschetz elements of Artinian Gorenstein algebras and hessians of homogeneous polynomials ⋮ Free extensions and Lefschetz properties, with an application to rings of relative coinvariants

Cites Work

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• Schubert calculus of a Coxeter group
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• The strong Lefschetz property of the coinvariant ring of the Coxeter group of type \(H_{4}\)
• Toward a numerical theory of ampleness
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• Basic sets of invariant polynomials for finite reflection groups

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