PIRSA:19050034

Video URL

https://pirsa.org/19050034

Algebraic Braids and Geometric Representation Theory

Trinh, M. (2019). Algebraic Braids and Geometric Representation Theory. Perimeter Institute for Theoretical Physics. https://pirsa.org/19050034

Trinh, Minh-Tam. Algebraic Braids and Geometric Representation Theory. Perimeter Institute for Theoretical Physics, May. 21, 2019, https://pirsa.org/19050034 

          @misc{ scivideos_PIRSA:19050034,
            doi = {10.48660/19050034},
            url = {https://pirsa.org/19050034},
            author = {Trinh, Minh-Tam},
            keywords = {Mathematical physics},
            language = {en},
            title = {Algebraic Braids and Geometric Representation Theory},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {may},
            note = {PIRSA:19050034 see, \url{https://scivideos.org/pirsa/19050034}}
          }

Minh-Tam Trinh University of Chicago

Talk numberPIRSA:19050034
DOI10.48660/19050034
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

In 2012, Maulik proved a conjecture of Oblomkov-Shende relating: (1) the Hilbert schemes of a plane curve (alternatively, its compactified Jacobian), (2) the HOMFLY polynomials of the links of its singularities. We recast his theorem from the viewpoint of representation theory. For a split semisimple group G with Weyl group W, we state a stronger conjecture relating two virtual modules over Lusztig's graded affine Hecke algebra,  constructed from: (1) fibers of a parabolic Hitchin map, (2) generalized Bott-Samelson spaces attached to conjugacy classes in the braid group of W. In arbitrary type, we can establish an infinite family of cases where it holds. Time permitting, we'll indicate how the new conjecture relates to P = W phenomena in nonabelian Hodge theory.