2021/05/27 by Gyenge, Ádám, Koppensteiner, Clemens, Logvinenko, Timothy · 1 citation
#14F08 (secondary) #18N25 (primary) #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2105.13334
Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical analogue of the Fock space representation of the Heisenberg algebra. Our construction generalises and unifies various categorical Heisenberg algebra actions appearing in the literature. In particular, we give a full categorical enhancement of the action on derived categories of symmetric quotient stacks introduced by Krug, which itself categorifies a Heisenberg algebra action proposed by Grojnowski.