Heisenberg algebra and a graphical calculus

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 vector spaces of morphisms between products of generating objects in this category.

45 pages, eps files

References in corpus (3)

• A diagrammatic approach to categorification of quantum groups I
• A functor-valued invariant of tangles
• Categorifications from planar diagrammatics

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