On the quotient ring by diagonal harmonics

Abstract

For a Weyl group W and its reflection representation mathfrak{h}, we find the character and Hilbert series for a quotient ring of C[mathfrak{h} oplus mathfrak{h}^*] by an ideal containing the W--invariant polynomials without constant term. This confirms conjectures of Haiman. The proof makes use of rational Cherednik algebras, as studied by Etingof and Ginzburg, and others.

References in corpus (3)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Principal Nilpotent pairs in a semisimple Lie algebra, I
• Finite dimensional representations of rational Cherednik algebras

Cited by in corpus (46)

• Finite dimensional representations of rational Cherednik algebras
• Higher Trivariate Diagonal Harmonics via generalized Tamari Posets
• Quantum Drinfeld Hecke Algebras
• Quasi-Invariants of Complex Reflection Groups
• Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r,p,n)
• Orthogonal functions generalizing Jack polynomials
• FI_W-modules and stability criteria for representations of the classical Weyl groups
• Affine Springer fibers of type A and combinatorics of diagonal coinvariants
• The center of small quantum groups I: the principal block in type A
• Poincare-Birkhoff-Witt Theorems
• Multivariate Diagonal Coinvariant Spaces for Complex Reflection Groups
• Affine Schubert calculus and double coinvariants
• Introduction to double Hecke algebras
• On category O for the rational Cherednik algebra of G(m,1,n): the almost semisimple case
• Cyclic sieving of noncrossing partitions for complex reflection groups
• ${\mathrm{FI}}_G$-modules, orbit configuration spaces, and complex reflection groups
• Character formulas and Bernstein-Gelfand-Gelfand resolutions for Cherednik algebra modules
• Diagonal Coinvariants and Double Affine Hecke Algebras
• Representations with minimal support for quantized Gieseker varieties
• A probabilistic interpretation of the Macdonald polynomials
• Hochschild cohomology and quantum Drinfeld Hecke algebras
• Rational Cherednik algebras and diagonal coinvariants of G(m,p,n)
• On some representations of the rational Cherednik algeba
• Groupes de réflexion, géométrie du discriminant et partitions non-croisées
• Affine Springer Fibers, Procesi bundles, and Cherednik algebras
• Shi arrangements and low elements in affine Coxeter groups
• Twisted quantum Drinfeld Hecke algebras
• Arc spaces and DAHA representations
• Exterior powers of the reflection representation in Springer theory
• Nested Hilbert schemes and the nested q,t-Catalan series
• Cyclic sieving and rational Catalan theory
• Coinvariants for modular representations of cyclic groups of prime order
• The diagonal coinvariant ring of a complex reflection group
• Double Macdonald polynomials as the stable limit of Macdonald superpolynomials
• Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector
• Alexander Duality and Rational Associahedra
• Representations of the rational Cherednik algebras of dihedral type
• Parking Structures: Fuss Analogs
• q,t-Fuss-Catalan numbers for finite reflection groups
• Additive and Multiplicative Coinvariant Spaces of Weyl Groups in the Light of Harmonics and Graded Transfer
• L'algèbre des invariants d'un groupe de Coxeter agissant sur un mutiple de sa représentation standard
• On Modular Invariants of A Vector and A Covector
• Diagonal invariants and genus-zero Hurwitz Frobenius manifolds
• Invariants of polynomials mod Frobenius powers
• Macdonald polynomials as characters of Cherednik algebra modules
• Weyl group $q$-Kreweras numbers and cyclic sieving