The Heisenberg category of a category – Ádám Gyenge (Alfréd Rényi Institute of Mathematics)


Department of Mathematics, Aula Magna.


The Heisenberg algebra associated with a lattice is a much-investigated object originating in quantum theory. Khovanov introduced
recently a categorification of the infinite Heisenberg algebra
associated with the free boson or, equivalently, a rank 1 lattice,
using a graphical construction involving planar diagrams. We extend
Khovanov’s graphical construction to derived categories of smooth and
projective varieties or, more generally, to categories having a Serre
functor. In our case, the underlying lattice will be the (numerical)
Grothendieck group of the category. We also obtain a 2-representation
of our Heisenberg category on a categorical analogue of the Fock
space. Joint work with Clemens Koppensteiner and Timothy Logvinenko.

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