Mathematische Zeitschrift

, Volume 288, Issue 1–2, pp 11–22 | Cite as

Symmetric quotient stacks and Heisenberg actions

  • Andreas Krug


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.



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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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of MarburgMarburgGermany

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