Parabolic Hilbert Schemes and Rational Cherednik Algebras

Explore a 51-minute lecture on parabolic Hilbert schemes and rational Cherednik algebras presented by Monica Vazirani at the Canada-Mexico-US Conference in Representation Theory, Noncommutative Algebra, and Categorification. Delve into the parameterization of irreducible representations of the symmetric group using Young diagrams and standard tableaux. Examine similar constructions for double affine Hecke algebra (DAHA) representations using periodic tableaux and rational Cherednik algebra representations with modifications. Investigate an alternate presentation of the rational DAHA and its Dunkl-Opdam subalgebra. Discover a geometric construction of the irreducible RCA module parameterized by the trivial Young diagram, utilizing the geometry of the parabolic Hilbert scheme of points on a plane curve singularity. Learn how the basis of equivariant homology from torus fixed points becomes the "tableau" basis in this context. Gain insights into joint work with Eugene Gorsky and José Simental on this topic.