PIRSA:19030119

Quantum Heisenberg categorification

Savage, A. (2019). Quantum Heisenberg categorification. Perimeter Institute. https://pirsa.org/19030119

Savage, Alistair. Quantum Heisenberg categorification. Perimeter Institute, Mar. 25, 2019, https://pirsa.org/19030119 

          @misc{ pirsa_PIRSA:19030119,
            doi = {10.48660/19030119},
            url = {https://pirsa.org/19030119},
            author = {Savage, Alistair},
            keywords = {Mathematical physics},
            language = {en},
            title = {Quantum Heisenberg categorification},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {mar},
            note = {PIRSA:19030119 see, \url{https://pirsa.org}}
          }

Alistair Savage University of Ottawa

DOI 10.48660/19030119
Collection
Talk Type Scientific Series
Subject

Abstract

The Heisenberg algebra plays a vital role in many areas of mathematics and physics.  We will describe a family of quantum Heisenberg categories, depending on a choice of central charge, that categorify this algebra.  When the central charge is nonzero, these categories act on modules for cyclotomic quotients of the affine Hecke algebra.  In central charge zero, we obtain an affinization of the HOMFLY-PT skein category, which acts on modules for $U_q(\mathfrak{gl}_n)$.  We will also discuss how the categories can be generalized by adding a Frobenius superalgebra into the construction.  This is joint work with Jon Brundan and Ben Webster.