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OverviewMotivated by the maximal subgroup problem of the finite classical groups the authors begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields $K$. A module of a group $G$ over $K$ is imprimitive, if it is induced from a module of a proper subgroup of $G$. The authors obtain their strongest results when ${\rm char}(K) = 0$, although much of their analysis carries over into positive characteristic. If $G$ is a finite quasisimple group of Lie type, they prove that an imprimitive irreducible $KG$-module is Harish-Chandra induced. This being true for $\mbox{\rm char}(K)$ different from the defining characteristic of $G$, the authors specialize to the case ${\rm char}(K) = 0$ and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. The authors determine the asymptotic proportion of the irreducible imprimitive $KG$-modules, when $G$ runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of their investigations is the fact that these proportions tend to $1$, if the Lie rank of the groups tends to infinity. For exceptional groups $G$ of Lie type of small rank, and for sporadic groups $G$, the authors determine all irreducible imprimitive $KG$-modules for arbitrary characteristic of $K$. Full Product DetailsAuthor: Gerhard Hiss , William J. Husen , Kay MagaardPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 234/1104 Weight: 0.200kg ISBN: 9781470409609ISBN 10: 1470409607 Pages: 114 Publication Date: 30 March 2015 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsAcknowledgements Introduction Generalities Sporadic groups and the Tits group Alternating groups Exceptional Schur multipliers and exceptional isomorphisms Groups of Lie type: Induction from non-parabolic subgroups Groups of Lie type: Induction from parabolic subgroups Groups of Lie type: ${\rm char}(K) = 0$ Classical groups: ${\rm char}(K) = 0$ Exceptional groups BibliographyReviewsAuthor InformationGerhard Hiss, Lehrstuhl D fur Mathematik, RWTH Aachen University, Germany. William J. Husen, Ohio State University, Columbus, OH, USA. Kay Magaard, University of Birmingham, UK. Tab Content 6Author Website:Countries AvailableAll regions |
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