Abstract
For every smooth projective variety X, we construct an action of the Heisenberg algebra on the direct sum of the Grothendieck groups of all the symmetric quotient stacks \([X^n/{\mathfrak {S}}_n]\) which contains the Fock space as a subrepresentation. The action is induced by functors on the level of the derived categories which form a weak categorification of the action.
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Acknowledgements
The author was financially supported by the research Grant KR 4541/1-1 of the DFG. He thanks Sabin Cautis, Daniel Huybrechts, Ciaran Meachan, David Ploog, Miles Reid, Pawel Sosna, and the referee for helpful comments.
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Krug, A. Symmetric quotient stacks and Heisenberg actions. Math. Z. 288, 11–22 (2018). https://doi.org/10.1007/s00209-017-1874-3
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DOI: https://doi.org/10.1007/s00209-017-1874-3