Heisenberg algebra and a graphical calculus
Volume 225 / 2014
Fundamenta Mathematicae 225 (2014), 169-210
MSC: 18D10, 19A22.
DOI: 10.4064/fm225-1-8
Abstract
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.
