Type: Seminar

Distribution: World

Expiry: 14 Apr 2022

CalTitle1: SMRI Algebra and Geometry Online: Vazirani -- From representations of the rational Cherednik algebra to parabolic Hilbert schemes via the Dunkl-Opdam subalgebra

Auth: hannahb@w63dq1n2.mcs.usyd.edu.au (hbry8683) in SMS-SAML

SMRI Algebra and Geometry Online ’From representations of the rational Cherednik algebra to parabolic Hilbert schemes via the Dunkl-Opdam subalgebra’ Monica Vazirani (University of California, Davis) Thursday, 14th April, 10:00am - 11:30am (AEST) Register: https://uni-sydney.zoom.us/meeting/register/tZAkf-qupj0oE9RKU8A9NcwUnEnoxXMHm6TT After registering, you will be sent a confirmation email ~24 hours prior to the seminar. Abstract: Young diagrams and standard tableaux on them parameterize irreducible representations of the symmetric group and their bases, respectively. There is a similar story for the double affine Hecke algebra (DAHA) taking periodic tableaux, or for the rational Cherednik algebra (a.k.a. rational DAHA) with appropriate modifications. This construction of the basis makes use of an alternate presentation of the rational DAHA and the basis diagonalizes the action of its Dunkl-Opdam subalgebra. We make use of the combinatorics to construct explicit maps between standard modules parameterized by hooks, thus recovering the BGG resolution of the simple module parameterized by the trivial hook. We can also describe this simple module using the geometry of parabolic Hilbert schemes of points on plane curve singularities. The ``tableau" basis that diagonalizes the Dunkl-Opdam subalgebra is the basis of equivariant homology that comes from torus fixed points. This is joint work with Eugene Gorsky and JosÃ© Simental. Biography: Monica Vazirani is a professor at UC Davis. She received her PhD from UC Berkeley, after which she had an NSF postdoc she spent at UC San Diego and UC Berkeley, as well as postdoctoral positions at MSRI and Caltech. Dr. Vazirani’s research interests center on the representation theory of algebras related to the symmetric group and how to express algebraic phenomena via the combinatorics of partitions, tableaux, crystal graphs and parking functions. Note: These seminars will be recorded, including participant questions (participants only when asking questions), and uploaded to the SMRI YouTube Channel https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI Other upcoming SMRI events can be found here: https://mathematical-research-institute.sydney.edu.au/news-events/