Vol. 14, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 5, 1025–1326
Issue 4, 777–1024
Issue 3, 521–775
Issue 2, 231–519
Issue 1, 1–230

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
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

We introduce a diagrammatic monoidal category eisk(z,t) which we call the quantum Heisenberg category; here, k is “central charge” and z and t are invertible parameters. Special cases were known before: for central charge k = 1 and parameters z = q q1 and t = z1 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 eis0(z,t) is the affinization of the HOMFLY-PT skein category. We also prove a basis theorem for the morphism spaces in eisk(z,t).

Heisenberg category, categorification, affine Hecke algebra
Mathematical Subject Classification 2010
Primary: 17B10
Secondary: 18D10
Received: 27 January 2019
Revised: 22 July 2019
Accepted: 2 September 2019
Published: 17 March 2020
Jonathan Brundan
Department of Mathematics
University of Oregon
Eugene, OR
United States
Alistair Savage
Department of Mathematics and Statistics
University of Ottawa
Ben Webster
Department of Pure Mathematics
University of Waterloo
Waterloo, ON
Perimeter Institute for Theoretical Physics
Waterloo, ON