The strong Lefschetz property of Gorenstein algebras generated by relative invariants
type: Item
instance of: scholarly article
title: The strong Lefschetz property of Gorenstein algebras generated by relative invariants
author: Takahiro Nagaoka
author: Akihito Wachi
published in: Proceedings of the American Mathematical Society
publication date: 2024-08-06T00:00:00Z
review text: The problem of determining Artinian Gorenstein algebras which have the strong Lefschetz property has been intensively studied. The authors consider Artinian Gorenstein algebras generated by the relative invariants of prehomogeneous vector spaces of commutative parabolic type. Determinants, determinants of symmetric matrices, and Pfaffians of alternating matrices of even size are some of the polynomials which belong to this family. They prove that these algebras have the strong Lefschetz property. The key ingredient in their study is the theory of generalized Verma modules of Lie algebras.
reviewed by: Anda-Georgina Olteanu
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 11S90
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 7892849
zbMATH Keywords: Lefschetz property
zbMATH Keywords: Gorenstein algebra
zbMATH Keywords: prehomogeneous vector space
zbMATH Keywords: relative invariant
MaRDI profile type: Publication
cites work: Q4863383
cites work: On higher Hessians and the Lefschetz properties
cites work: On cubic hypersurfaces with vanishing Hessian
cites work: Lefschetz properties for Artinian Gorenstein algebras presented by quadrics
cites work: On mixed Hessians and the Lefschetz properties
cites work: The Lefschetz properties
cites work: Sperner property and finite-dimensional Gorenstein algebras associated to matroids
cites work: Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups
cites work: Lefschetz elements of Artinian Gorenstein algebras and hessians of homogeneous polynomials
cites work: Structure of prehomogeneous spaces associated with certain graded Lie algebras
cites work: Strictness of the log-concavity of generating polynomials of matroids
cites work: Strict log-concavity of the Kirchhoff polynomial and its applications
cites work: Strict log-concavity of the Kirchhoff polynomial and its applications to the strong Lefschetz property
cites work: Q4843377
cites work: Opérateurs différentiels de Shimura et espaces préhomogènes. (Shimura differential operators and prehomogeneous spaces)
cites work: A classification of irreducible prehomogeneous vector spaces and their relative invariants
cites work: Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen
cites work: Contravariant forms on generalized Verma modules and \(b\)-functions
DOI: 10.1090/PROC/16870
description: scientific article; zbMATH DE number 7892849