PIRSA:20060035

Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra

APA

Gorsky, E. (2020). Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra. Perimeter Institute. https://pirsa.org/20060035

MLA

Gorsky, Eugene. Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra. Perimeter Institute, Jun. 25, 2020, https://pirsa.org/20060035

BibTex

          @misc{ pirsa_20060035,
            doi = {10.48660/20060035},
            url = {https://pirsa.org/20060035},
            author = {Gorsky, Eugene},
            keywords = {Mathematical physics},
            language = {en},
            title = {Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {jun},
            note = {PIRSA:20060035 see, \url{https://pirsa.org}}
          }
          

Eugene Gorsky University of California - Davis (UCD)

Abstract

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 José Simental and Monica Vazirani.