Vol. 14, No. 2, 2020

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On the definition of quantum Heisenberg category

Jonathan Brundan, Alistair Savage and Ben Webster

Vol. 14 (2020), No. 2, 275–321
Abstract

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).

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