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Motivated 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 $K$.

Product Specifications

Format: paperback
ASIN: 1470409607
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 March 2015
Listed Since: 05 December 2014

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Imprimitive Irreducible Modules for Finite Quasisimple Groups (Memoirs of the American Mathematical Society)

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It has never been this cheap. We have no record of a lower price.

Imprimitive Irreducible Modules for Finite Quasisimple Groups (Memoirs of the American Mathematical Society)

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