Theory of prehomogeneous vector spaces without regularity condition

DOI10.2977/prims/1195169004zbMath0773.14025OpenAlexW2129715853MaRDI QIDQ1187172

Akihiko Gyoja

Publication date: 28 June 1992

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195169004

zbMATH Keywords

Fourier transform\(D\)-modulescomplex prehomogeneous vector spaces

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Group actions on varieties or schemes (quotients) (14L30) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Almost homogeneous manifolds and spaces (32M12)

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Highest weight modules and \(b\)-functions of semi-invariants ⋮ Theory of prehomogeneous vector spaces. II: A supplement ⋮ LOCAL FUNCTIONAL EQUATIONS ATTACHED TO THE POLARIZATIONS OF HOMALOIDAL POLYNOMIALS ⋮ Character sums and intersection cohomology complexes associated to the space of square matrices ⋮ Decompositions of Bernstein-Sato polynomials and slices ⋮ Holonomic functions and prehomogeneous spaces ⋮ \(b\)-functions associated with quivers of type \textsf{A} ⋮ Dimension formulas for the hyperfunction solutions to holonomic \(\mathcal D\)-modules ⋮ The fundamental theorem of prehomogeneous vector spaces modulo $p^m$ (With an appendix by F. Sato) ⋮ Extensions of modules over Weyl algebras ⋮ The \(b\)-functions of semi-invariants of quivers ⋮ On categories of equivariant \(\mathcal{D}\)-modules ⋮ Bernstein polynomials and spectral numbers for linear free divisors ⋮ \(b\)-functions of the prehomogeneous vector space arising from a cuspidal character sheaf of \(E_7\) ⋮ Characteristic cycles of perverse sheaves and Milnor fibers ⋮ MULTIPLICITY ONE PROPERTY AND THE DECOMPOSITION OF b-FUNCTIONS ⋮ Singularities of zero sets of semi-invariants for quivers ⋮ Further generalization of generalized Verma modules ⋮ Certain unipotent representations of finite Chevalley groups and Picard–Lefschetz monodromy

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