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The trace (or zeroth Hochschild homology) of Khovanov’s Heisenberg category is identified with a quotient of the algebra $$W_{1+\infty }$$. This induces an action of $$W_{1+\infty }$$ on the center of the categorified Fock space representation, which can be identified with the action of $$W_{1+\infty }$$ on symmetric functions.
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The degenerate Heisenberg category and its Grothendieck ring
The degenerate Heisenberg category Heis_k is a strict monoidal category which was originally introduced in the special case k=-1 by Khovanov in 2010. Khovanov conjectured that the Grothendieck ring of the additive Karoubi envelope of his category is isomorphic to a certain \Z-form for the universal enveloping algebra of the infinite-dimensional Heisenberg Lie algebra specialized at central charge -1. We prove this conjecture and extend it to arbitrary central charge k. We also explain how to categorify the comultiplication (generically).
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- Award ID(s):
- 2101783
- PAR ID:
- 10511882
- Publisher / Repository:
- Centre Mersenne
- Date Published:
- Journal Name:
- Annales Scientifiques de l'École Normale Supérieure
- ISSN:
- 0012-9593
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.24033/asens.2560
