Imprimitive irreducible modules for finite quasisimple groups / Gerhard Hiss, William J. Husen and Kay Magaard.
By: Hiss, Gerhard.
Contributor(s): Husen, William J [author]  Magaard, Kay [author].
Material type: TextSeries: Memoirs of the American Mathematical Society ; v 234, no 1104.Publisher: Providence : American Mathematical Society, 2015Description: v, 114 p. ; 26 cm.ISBN: 9781470409609 (pbk. : acidfree paper).Subject(s): Algebraic fields  Finite groups  Semisimple Lie groupsDDC classification: 510Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

510 Am512 (Browse shelf)  Available  136687 
Includes bibliographical references.
Chapter 1. Introduction
Chapter 2. Generalities
Chapter 3. Sporadic Groups and the Tits Group
Chapter 4. Alternating Groups
Chapter 5. Exceptional Schur Multipliers and Exceptional Isomorphisms
Chapter 6. Groups of Lie type: Induction from nonparabolic subgroups
Chapter 7. Groups of Lie type: Induction from parabolic subgroups
Chapter 8. Groups of Lie type: char$(K) = 0$
Chapter 9. Classical groups: $\text {char}(K) = 0$
Chapter 10. Exceptional groups
Bibliography.
Motivated by the maximal subgroup problem of the finite classical groups we 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. We obtain our strongest results when char(K) = 0, although much of our analysis carries over into positive characteristic. If G is a finite quasisimple group of Lie type, we prove that an imprimitive irreducible KGmodule is HarishChandra induced. This being true for char(K) different from the defining characteristic of G, we specialize to the case char(K) = 0 and apply HarishChandra philosophy to classify irreducible HarishChandra induced modules in terms of HarishChandra series, as well as in terms of Lusztig series. We determine the asymptotic proportion of the irreducible imprimitive KGmodules, when G runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of our 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, we determine all irreducible imprimitive KGmodules for arbitrary characteristic of K.
There are no comments for this item.