Lie Groups Seminar

Peter SamuelsonUniversity of Edinburgh
Khovanov's Heisenberg category and the elliptic Hall algebra

Friday, September 29, 2017 - 3:30pm
Malott 406

Khovanov defined a monoidal category H using induction and restriction
functors between symmetric groups so that the K-theory K(H) is the
Heisenberg algebra, and this category was given a q-deformation H_q by
Licata and Savage. In this talk we describe the trace Tr(H_q) (i.e.
the Hochschild homology), which is an algebra which contains K(H_q)
but is much larger. This description implies it is isomorphic to a
specialization of the Hall algebra of the category of coherent sheaves
over an elliptic curve. (Joint work with Cautis, Lauda, Licata, and
Sussan.)