Jonathan Brundan
Published 2017-09-19Version 1
We revisit the definition of the Heisenberg category of level k. In level -1, this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. In other negative levels, the definition is due to Mackaay and Savage, also with some redundant relations, while the level zero case is the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients.
A basis theorem for the affine oriented Brauer category and its cyclotomic quotients
On the definition of Kac-Moody 2-category
Embedding Deligne's category $\mathrm{Rep}(S_t)$ in the Heisenberg category
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