Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification

JOURNAL OF ALGEBRA

卷:505

Article

Mackaay, Marco^1,2  Savage, Alistair³ 

[1] Univ Algarve, Dept Matemat, Algarve, Portugal

[2] Inst Super Tecn, CAMGSD, Lisbon, Portugal

[3] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

关键词: Categorification;    Heisenberg algebra;    Hecke algebras;    Cyclotomic quotients;    Diagrammatic calculus;   

DOI  :  10.1016/j.jalgebra.2018.03.004

来源: Elsevier

【 摘 要 】

We associate a monoidal category H-lambda to each dominant integral weight lambda of sl(p) or sl(infinity). These categories, defined in terms of planar diagrams, act naturally on categories of modules for the degenerate cyclotomic Hecke algebras associated to lambda. We show that, in the sl infinity case, the level d Heisenberg algebra embeds into the Grothendieck ring of H-lambda, where d is the level of lambda. The categories H-lambda can be viewed as a graphical calculus describing induction and restriction functors between categories of modules for degenerate cyclotomic Hecke algebras, together with their natural transformations. As an application of this tool, we prove a new result concerning centralizers for degenerate cyclotomic Hecke algebras. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free