Hecke algebras, finite general linear groups, and Heisenberg categorification

Details Hecke algebras, finite general linear groups, and Heisenberg categorification Hecke algebras, finite general linear groups, and Heisenberg categorification

2011-01-02

arxiv.org/abs/1101.0420v2

Mathematics

Representation Theory

46 pages, many figures; v2: Some formulas corrected and additional explanations added

Scientific paper

We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined by Khovanov, acts naturally on the categories of modules for Hecke algebras of type A and finite general linear groups. In this way, we obtain a categorification of the bosonic Fock space. We also develop the theory of parabolic induction and restriction functors for finite groups and prove general results on biadjointness and cyclicity in this setting.

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