Hecke algebras, finite general linear groups, and Heisenberg categorification

被引:27
作者
Licata, Anthony [1 ]
Savage, Alistair [2 ]
机构
[1] Stanford Univ, Dept Math, Bldg 380,450 Serra Mall, Stanford, CA 94305 USA
[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Categorification; Heisenberg algebra; Hecke algebra; planar diagrammatics; finite general linear groups;
D O I
10.4171/QT/37
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:125 / 185
页数:61
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