The Categorified Heisenberg Algebra I: A Combinatorial Representation

Abstract

We give an introductory account of Khovanov's categorification of the Heisenberg algebra, and construct a combinatorial model for it in a 2-category of spans of groupoids. We also treat a categorification of $U(s{l}_n)$ in a similar way. These give rise to standard representations on vector spaces through a linearization process.

37 pages; v2 adds new theorems, examples, improved proofs

References in corpus (3)

• 2-Kac-Moody algebras
• Compact Closed Bicategories
• Groupoidification Made Easy

Cited by in corpus (5)

• Compact Closed Bicategories
• Groupoid Semantics for Thermal Computing
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• A groupoidification of the fermion algebra