The invariant holonomic system on a semisimple Lie algebra

DOI10.1007/BF01388568zbMath0538.22013OpenAlexW2100332131WikidataQ115393644 ScholiaQ115393644MaRDI QIDQ793164

Masaki Kashiwara, Ryoshi Hotta

Publication date: 1984

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

Full work available at URL: https://eudml.org/doc/143100

zbMATH Keywords

Riemann-Hilbert correspondenceregular holonomic systemSpringer representationsinvariant eigendistributionsgeometric Weyl group representationsintersection cohomology complexinvariant holonomic system

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items

Generalized Springer theory for \(D\)-modules on a reductive Lie algebra, \({\mathfrak G}\)-module, Springer's representations and bivariant Chern classes, \(D\)-modules and representation theory of Lie groups, Totally Aspherical Parameters for Cherednik Algebras, Local cohomology modules of \(A\)-hypergeometric system of Cohen-Macaulay type, Perverse schobers and birational geometry, On the regularity of \(D\)-modules generated by relative characters, Formal extension and quotients of the invariant holonomic system, Elliptic Springer theory, Microlocalisation of $\cal{D}$-modules along a submanifold, Macdonald positivity via the Harish-Chandra \(D\)-module, Traces on finite \(\mathcal{W}\)-algebras, Some combinatorial identities related to commuting varieties and Hilbert schemes, Microlocal \(KZ\)-functors and rational Cherednik algebras., Howe correspondence and Springer correspondence for real reductive dual pairs, The orders of invariant eigendistributions, Unnamed Item, Isospectral commuting variety, the Harish-Chandra \(\mathcal D\)-module, and principal nilpotent pairs, Irregularity of hypergeometric systems via slopes along coordinate subspaces, Invariant eigendistributions on a semisimple Lie algebra and homology classes on the conormal variety. II: Representations of Weyl groups, The kernel of an homomorphism of Harish-Chandra, Hamiltonian reduction and nearby cycles for mirabolic \(\mathcal{D}\)-modules, A geometric Schur functor., Invariant distributions supported on the nilpotent cone of a semisimple Lie algebra, Limit formulas for groups with one conjugacy class of Cartan subgroups, Perverse sheaves on rank stratifications, Characteristic cycles for the loop Grassmannian and nilpotent orbits., Parabolic induction and the Harish-Chandra D-module, Index of transversally elliptic -modules, Cohomology of the minimal nilpotent orbit, Invariant Differential Operators on a Reductive Lie Algebra and Weyl Group Representations, Unnamed Item, Microlocalization of rational Cherednik algebras, Integral transforms with exponential kernels and Laplace transform, Poisson traces, D-modules, and symplectic resolutions, Filtrations on Springer fiber cohomology and Kostka polynomials, Fourier transform and the Iwahori-Matsumoto involution, A homomorphism of Harish-Chandra and direct images of $\mathcal {D}$-modules, A unipotent support for irreducible representations, On categories of equivariant \(\mathcal{D}\)-modules, \({\mathcal D}\)-modules and characters of semisimple Lie groups, Closed formulae for a \(b\)-function associated with a weighted homogeneous isolated complete intersection singularity, Polynômes de Joseph et représentation de Springer, On the vanishing of some non-semisimple orbital integrals, A topological approach to induction theorems in Springer theory, Semisimplicity of the category of admissible \(\mathcal{D}\)-modules, Invariant differential operators on the tangent space of some symmetric spaces, $C^{-\infty}$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations, Springer theory via the Hitchin fibration, Equivariant \(D\)-modules attached to nilpotent orbits in a semisimple Lie algebra, The geometric nature of the fundamental lemma, Two geometric character formulas for reductive Lie groups, Characters of finite reductive groups and \(D\)-modules., A limit formula for elliptic orbital integrals, La transformation de Fourier pour les \({\mathcal D}\)-modules. (Fourier transform for \({\mathcal D}\)-modules), On the orbit method and the homomorphism of Harish-Chandra, On Joseph's construction of Weyl group representations, Gauss sums of prehomogeneous vector spaces, A counterexample to a problem on commuting matrices, On the irreducibility of the commuting variety of a reductive symmetric pair of rank 1, Differential operators on homogeneous spaces. III: Characteristic varieties of Harish Chandra modules and of primitive ideals, Characteristic cycles of certain character sheaves

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