对:赫克代数，有限一般线性群，和海森堡分类的勘误

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2011-01-02 DOI:10.4171/QT/37

Anthony M. Licata, Alistair Savage

{"title":"对:赫克代数，有限一般线性群，和海森堡分类的勘误","authors":"Anthony M. Licata, Alistair Savage","doi":"10.4171/QT/37","DOIUrl":null,"url":null,"abstract":"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 typeA 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. Mathematics Subject Classification (2010). Primary: 20C08, 17B65; Secondary: 16D90.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"60 1","pages":"183-183"},"PeriodicalIF":1.0000,"publicationDate":"2011-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"46","resultStr":"{\"title\":\"Erratum to: Hecke algebras, finite general linear groups, and Heisenberg categorification\",\"authors\":\"Anthony M. Licata, Alistair Savage\",\"doi\":\"10.4171/QT/37\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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 typeA 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. Mathematics Subject Classification (2010). Primary: 20C08, 17B65; Secondary: 16D90.\",\"PeriodicalId\":51331,\"journal\":{\"name\":\"Quantum Topology\",\"volume\":\"60 1\",\"pages\":\"183-183\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2011-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"46\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/QT/37\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/QT/37","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 46

摘要

我们定义了一类平面图，其Grothendieck群包含无限秩Heisenberg代数的一个积分版本，从而得到了这个代数的一个范畴。我们的范畴是Khovanov定义的范畴的q-变形，它自然地作用于a型Hecke代数和有限一般线性群的模的范畴。通过这种方法，我们得到了玻色子Fock空间的一个分类。我们还发展了有限群的抛物型诱导和限制函子理论，并证明了在这种情况下关于双伴随性和环性的一般结果。数学学科分类(2010)。初级:20C08, 17B65;二级:16 d90。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Erratum to: Hecke algebras, finite general linear groups, and Heisenberg categorification

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 typeA 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. Mathematics Subject Classification (2010). Primary: 20C08, 17B65; Secondary: 16D90.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.