PIRSA:19050034

Algebraic Braids and Geometric Representation Theory

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

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

          @misc{ pirsa_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},
            year = {2019},
            month = {may},
            note = {PIRSA:19050034 see, \url{https://pirsa.org}}
          }

Minh-Tam Trinh

University of Chicago

Talk number
PIRSA:19050034
Collection
Talk Type
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.