The Heisenberg category and elliptic Hall algebra
Date:
Thursday, May 4, 2017 14:45 - 16:45
Speaker:
Peter Samuelson (University of Edinburgh)
Location:
Seminar room Big Ground floor / Office Bldg West (I21.EG.101)
Series:
Mathematics and CS Seminar
Host:
Tamas Hausel
Contact:
DE ANTONI Jessica
The Heisenberg category H is a monoidal category defined by Khovanov using representation theory of symmetric groups (a deformation H_q was given by Licata and Savage using Hecke algebras). Both H and H_q categorify the Heisenberg algebra. The Hochschild homology (or, trace) of H_q is an algebra, and we show it is a specialization of the elliptic Hall algebra E. In this setting, the action of E on symmetric functions comes from a 2-representation of H_q defined using Hecke algebras. (This is joint work with Cautis, Lauda, Licata, and Sussan.)