Rational Cherednik algebras and Hilbert schemes. II: Representations and sheaves

DOI10.1215/S0012-7094-06-13213-1zbMath1096.14003arXivmath/0410293MaRDI QIDQ2492110

J. Toby Stafford, Iain C.Gordon

Publication date: 6 June 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410293

zbMATH Keywords

Verma modulesMorita equivalenceKostka numbersProcesi bundle

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Module categories in associative algebras (16D90) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Parametrization (Chow and Hilbert schemes) (14C05) Deformations of associative rings (16S80)

Related Items

Mirabolic Langlands duality and the quantum Calogero-Moser system ⋮ \(\mathcal{N} = 2\) gauge theories, instanton moduli spaces and geometric representation theory ⋮ Knot homology and sheaves on the Hilbert scheme of points on the plane ⋮ Quantization of minimal resolutions of Kleinian singularities. ⋮ The Auslander-Gorenstein property for \(\mathbb Z\)-algebras ⋮ Lectures on knot homology ⋮ Arc spaces and DAHA representations ⋮ Microlocal \(KZ\)-functors and rational Cherednik algebras. ⋮ Exterior powers of the reflection representation in Springer theory ⋮ Derived equivalence for quantum symplectic resolutions ⋮ Refined knot invariants and Hilbert schemes ⋮ Microlocalization of rational Cherednik algebras ⋮ The Hilbert scheme of a plane curve singularity and the \textsc{HOMFLY} homology of its link ⋮ Macdonald polynomials as characters of Cherednik algebra modules ⋮ Cherednik algebras and Hilbert schemes in characteristic 𝑝 ⋮ The Dunkl weight function for rational Cherednik algebras ⋮ Parameters for generalized Hecke algebras in type B ⋮ Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras ⋮ Hilbert schemes and noncommutative deformations of type A Kleinian singularities ⋮ Rational Cherednik algebras and Hilbert schemes

Cites Work

• Differential operators on homogeneous spaces. III: Characteristic varieties of Harish Chandra modules and of primitive ideals
• Kazhdan-Lusztig conjecture and holonomic systems
• Projective modules in the category \(\mathcal O\) for the Cherednik algebra.
• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• On the quotient ring by diagonal invariants.
• Cherednik algebras and differential operators on quasi-invariants.
• On the category \(\mathcal O\) for rational Cherednik algebras.
• \(t,q\)-Catalan numbers and the Hilbert scheme.
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Certain invariant subrings are Gorenstein. I
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• Some natural bigraded \(S_ n\)-modules and \(q,t\)-Kostka coefficients
• Instantons and affine algebras. I: The Hilbert scheme and vertex operators
• On the decomposition matrices of the quantized Schur algebra
• Rational Cherednik algebras and Hilbert schemes
• The McKay correspondence as an equivalence of derived categories
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• Invariant Differential Operators on a Reductive Lie Algebra and Weyl Group Representations
• Modules of t-Finite Vectors Over Semi-Simple Lie Algebras
• The Integrability of the Characteristic Variety
• Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes
• Représentations de dimension finie de l’algèbre de Cherednik rationnelle
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item