Corpus ID: 216914238

Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra

@article{Gorsky2020ParabolicHS,
  title={Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra},
  author={E. Gorsky and J. Simental and M. Vazirani},
  journal={arXiv: Representation Theory},
  year={2020}
}
In this note we explicitly construct an action of the rational Cherednik algebra $H_{1,m/n}(S_n,\mathbb{C}^n)$ corresponding to the permutation representation of $S_n$ on the $\mathbb{C}^{*}$-equivariant homology of parabolic Hilbert schemes of points on the plane curve singularity $\{x^{m} = y^{n}\}$ for coprime $m$ and $n$. We use this to construct actions of quantized Gieseker algebras on parabolic Hilbert schemes on the same plane curve singularity, and actions of the Cherednik algebra at… Expand

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References

SHOWING 1-10 OF 53 REFERENCES
Dunkl operators for complex reflection groups
Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameterized family of deformations of the polynomial De Rham complex. This leads toExpand
There exist a ∈ a and t ∈ R such that the stabilizer of a in G K is the Iwahori subgroup G K,a = I
    USEFUL OPERATORS ON REPRESENTATIONS OF THE RATIONAL CHEREDNIK ALGEBRA OF TYPE 𝔰𝔩 n
    Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra Hn(c) of type sln, which areExpand
    The spherical part of the local and global Springer actions
    The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In this paper, we showExpand
    Unitary representations of cyclotomic rational Cherednik algebras
    We classify the irreducible unitary modules in category O for the rational Cherednik algebras of type G(r,1,n) and give explicit combinatorial formulas for their graded characters. More precisely, weExpand
    Orthogonal functions generalizing Jack polynomials
    The rational Cherednik algebra ℍ is a certain algebra of differential-reflection operators attached to a complex reflection group W and depending on a set of central parameters. Each irreducibleExpand
    Purity of equivalued affine Springer fibers
    The affine Springer fiber corresponding to a regular integral equivalued semisimple element admits a paving by vector bundles over Hessenberg varieties and hence its (Borel-Moore) homology is "pure".
    Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra
    We give an alternate presentation of the cyclotomic rational Cherednik algebra, which has the useful feature of compatibility with the Opdam-Dunkl subalgebra. This presentation has a diagrammaticExpand
    Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, I
    Consider the 3-dimensional N = 4 supersymmetric gauge theory associated with a compact Lie group G and its quaternionic representation M. Physicists study its Coulomb branch, which is a noncompactExpand
    Geometric representations of graded and rational Cherednik algebras
    We provide geometric constructions of modules over the graded Cherednik algebra $\mathfrak{H}^{gr}_\nu$ and the rational Cherednik algebra $\mathfrak{H}^{rat}_\nu$ attached to a simple algebraicExpand
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