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Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Thursday, July 15, 12:00 ~ 12:35 UTC-3

Parabolic Hilbert schemes and rational Cherednik algebras

Monica Vazirani

UC Davis, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

One can use the geometry of parabolic Hilbert schemes of points on plane curve singularities to build representations of the rational Cherednik algebra (RCA) in type A. We use an alternate presentation of the RCA to describe these geometric representations. The basis of equivariant homology that comes from torus fixed points has a nice combinatorial description; and furthermore, this basis diagonalizes the action of the Dunkl-Opdam subalgebra of the RCA. We make use of our explicit combinatorial bases as well as the alternate presentation to construct explicit maps between standard modules parameterized by hooks, thus recovering the BGG resolution of the simple module parameterized by the trivial hook.

Joint work with Eugene Gorsky (UC Davis) and José Simental (Max-Planck-Institut für Mathematik).

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