ALGEBRAIC COMBINATORICS

no. 4
On the definition of Heisenberg category
Brundan, Jonathan1
1 Department of Mathematics University of Oregon Eugene OR 97403 USA
Algebraic Combinatorics, Volume 1 (2018) no. 4, pp. 523-544.

We revisit the definition of the Heisenberg category of central charge k∈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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.26
Classification: 17B10, 18D10
Keywords: Heisenberg category, string calculus
Brundan, Jonathan 1

1 Department of Mathematics University of Oregon Eugene OR 97403 USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/articles/10.5802/alco.26/

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