# ALGEBRAIC COMBINATORICS

On the definition of Heisenberg category
Algebraic Combinatorics, Volume 1 (2018) no. 4, pp. 523-544.

We revisit the definition of the Heisenberg category of central charge $k\in ℤ$. For central charge $-1$, this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. For other negative central charges, the definition is due to Mackaay and Savage, also with some redundant relations, while central charge zero recovers the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients.

Revised: 2018-05-22
Accepted: 2018-06-12
Published online: 2018-09-10
DOI: https://doi.org/10.5802/alco.26
Classification: 17B10,  18D10
Keywords: Heisenberg category, string calculus
@article{ALCO_2018__1_4_523_0,
author = {Brundan, Jonathan},
title = {On the definition of Heisenberg category},
journal = {Algebraic Combinatorics},
publisher = {MathOA foundation},
volume = {1},
number = {4},
year = {2018},
pages = {523-544},
doi = {10.5802/alco.26},
mrnumber = {3875075},
zbl = {06963903},
language = {en},
url = {alco.centre-mersenne.org/item/ALCO_2018__1_4_523_0/}
}
Brundan, Jonathan. On the definition of Heisenberg category. Algebraic Combinatorics, Volume 1 (2018) no. 4, pp. 523-544. doi : 10.5802/alco.26. https://alco.centre-mersenne.org/item/ALCO_2018__1_4_523_0/

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