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- Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra

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20060035

In this note we give an alternative presentation of the rational

Cherednik algebra H_c corresponding to the permutation representation of

S_n. As an application, we give an explicit combinatorial basis for all

standard and simple modules if the denominator of c is at least n, and

describe the action of H_c in this basis. We also give a basis for the

irreducible quotient of the polynomial representation and compare it to

the basis of fixed points in the homology of the parabolic Hilbert

scheme of points on the plane curve singularity {x^n=y^m}. This is a

joint work with JosÃ© Simental and Monica Vazirani.

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©2012 Perimeter Institute for Theoretical Physics