Heisenberg algebra and a graphical calculus

By Mikhail Khovanov. 2010

112 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e5711694e7d68eaf2adf81deab73c873b17f0c32

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Erratum to: Hecke algebras, finite general linear groups, and Heisenberg categorification (2011, background): “This composition is precisely the map 0 of [11], which is injective by [11], Proposition 3.”
Quiver Schur algebras and q-Fock space (2011, background): “This is especially intriguing and promising given the various interesting categorification of Heisenberg algebras ([CL10], [Kho10], [LS11]) which appeared recently in the literature.”
Heisenberg categorification and Hilbert schemes (2010, background): “[FKM] I. Frenkel, M. Khovanov and A. Malkin, unpublished notes, circa 2003.”
An introduction to diagrammatic algebra and categorified quantum sl(2) (2011, background): “See [2] for a discussion on the relationship between higher categories and higher dimensional diagrams and [34] for a survey on the relationship between planar diagrammatics and categorification.”