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The Categorified Heisenberg Algebra I: A Combinatorial Representation (1207.2054v2)
Published 9 Jul 2012 in math.QA and math.CT
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 $U(sl_n)$ in a similar way. These give rise to standard representations on vector spaces through a linearization process.