Heisenberg algebra and a graphical calculus. (English) Zbl 1304.18019

Khovanov, Mikhail

Fundam. Math. 225, 169-210 (2014).

Summary: A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of the vector spaces of morphisms between products of generating objects in this category.

MSC:

18D10	Monoidal, symmetric monoidal and braided categories (MSC2010)
17B65	Infinite-dimensional Lie (super)algebras
19A22	Frobenius induction, Burnside and representation rings

Keywords:

categorification of Heisenberg algebra; biadjoint functors; symmetric groups; induction and restriction functors; graphical calculus