Imprimitive Irreducible Modules for Finite Quasisimple Groups (eBook)

Gerhard Hiss (Autor)

eBook Download: PDF

2015
114 Seiten
American Mathematical Society (Verlag)
978-1-4704-2031-4 (ISBN)

Infos

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 $K$.

Produkt-Details

• Erscheint lt. Verlag: 2.6.2015
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-2031-7 / 1470420317
• ISBN-13: 978-1-4704-2031-4 / 9781470420314