PIRSA:19010068

Categorical Bernstein Operators and the Boson-Fermion correspondence.

Sandoval Gonzalez, N. (2019). Categorical Bernstein Operators and the Boson-Fermion correspondence. . Perimeter Institute. https://pirsa.org/19010068

Sandoval Gonzalez, Nicolle. Categorical Bernstein Operators and the Boson-Fermion correspondence. . Perimeter Institute, Jan. 17, 2019, https://pirsa.org/19010068 

          @misc{ pirsa_PIRSA:19010068,
            doi = {10.48660/19010068},
            url = {https://pirsa.org/19010068},
            author = {Sandoval Gonzalez, Nicolle},
            keywords = {Mathematical physics},
            language = {en},
            title = {Categorical Bernstein Operators and the Boson-Fermion correspondence. },
            publisher = {Perimeter Institute},
            year = {2019},
            month = {jan},
            note = {PIRSA:19010068 see, \url{https://pirsa.org}}
          }

Nicolle Sandoval Gonzalez

University of California, Los Angeles

Talk number
PIRSA:19010068
Collection
Talk Type
Subject
Abstract

Bernstein operators are vertex operators that create and annihilate Schur polynomials. These operators play a significant role in the mathematical formulation of the Boson-Fermion correspondence due to Kac and Frenkel. The role of this correspondence in mathematical physics has been widely studied as it bridges the actions of the infinite Heisenberg and Clifford algebras on Fock space. Cautis and Sussan conjectured a categorification of this correspondence within the framework of Khovanov's Heisenberg category. I will discuss how to categorify the Bernstein operators and settle the Cautis-Sussan conjecture, thus proving a categorical Boson-Fermion correspondence.