Imprimitive Irreducible Modules for Finite Quasisimple Groups is popular PDF and ePub book, written by Gerhard Hiss in 2015-02-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Imprimitive Irreducible Modules for Finite Quasisimple Groups can be Read Online from any device for your convenience.
Imprimitive Irreducible Modules for Finite Quasisimple Groups Book PDF Summary
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 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 \rm char(K) different from the defining characteristic of G, the authors specialize to the case 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.
Detail Book of Imprimitive Irreducible Modules for Finite Quasisimple Groups PDF
- Author : Gerhard Hiss
- Release : 06 February 2015
- Publisher : American Mathematical Soc.
- ISBN : 9781470409609
- Genre : Mathematics
- Total Page : 126 pages
- Language : English
- PDF File Size : 10,9 Mb
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