On the definition of quantum Heisenberg category

Brundan, Jonathan; Savage, Alistair; Webster, Ben

doi:10.2140/ant.2020.14.275

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

On the definition of quantum Heisenberg category

Jonathan Brundan, Alistair Savage and Ben Webster

Vol. 14 (2020), No. 2, 275–321

DOI: 10.2140/ant.2020.14.275

Abstract

We introduce a diagrammatic monoidal category $ℋ e i s_{k} (z, t)$ which we call the quantum Heisenberg category; here, $k \in ℤ$ is “central charge” and $z$ and $t$ are invertible parameters. Special cases were known before: for central charge $k = - 1$ and parameters $z = q - q^{- 1}$ and $t = - z^{- 1}$ our quantum Heisenberg category may be obtained from the deformed version of Khovanov’s Heisenberg category introduced by Licata and Savage by inverting its polynomial generator, while $ℋ e i s_{0} (z, t)$ is the affinization of the HOMFLY-PT skein category. We also prove a basis theorem for the morphism spaces in $ℋ e i s_{k} (z, t)$ .

Keywords

Heisenberg category, categorification, affine Hecke algebra

Mathematical Subject Classification 2010

Primary: 17B10

Secondary: 18D10

Milestones

Received: 27 January 2019

Revised: 22 July 2019

Accepted: 2 September 2019

Published: 17 March 2020

Authors

Jonathan Brundan
Department of Mathematics University of Oregon Eugene, OR United States

Alistair Savage
Department of Mathematics and Statistics University of Ottawa ON Canada

Ben Webster
Department of Pure Mathematics University of Waterloo Waterloo, ON Canada	Perimeter Institute for Theoretical Physics Waterloo, ON Canada

Vol. 14, No. 2, 2020