Irreducibility of Disconnected Subgroups of Exceptional Algebraic Groups
Author: Soumaïa Nadia Ghandour
Publisher:
Published: 2008
Total Pages: 121
ISBN-13:
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Author: Soumaïa Nadia Ghandour
Publisher:
Published: 2008
Total Pages: 121
ISBN-13:
DOWNLOAD EBOOKAuthor: Adam R. Thomas
Publisher: American Mathematical Soc.
Published: 2021-06-18
Total Pages: 191
ISBN-13: 1470443376
DOWNLOAD EBOOKThis paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
Author: Donna M. Testerman
Publisher: American Mathematical Soc.
Published: 1988
Total Pages: 198
ISBN-13: 0821824538
DOWNLOAD EBOOKLet [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on some rational [italic]k[italic]Y module [italic]V. This extends work of Dynkin who obtained a similar classification for algebraically closed fields of characteristic 0. The main result has been combined with work of G. Seitz to obtain a classification of the maximal closed connected subgroups of the classical algebraic groups defined over [italic]k.
Author: Timothy C. Burness
Publisher: American Mathematical Soc.
Published: 2015-06-26
Total Pages: 122
ISBN-13: 147041046X
DOWNLOAD EBOOKLet be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.
Author: Timothy C. Burness,
Publisher: American Mathematical Soc.
Published: 2016-01-25
Total Pages: 100
ISBN-13: 1470414945
DOWNLOAD EBOOKLet be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .
Author: Gary M. Seitz
Publisher: American Mathematical Soc.
Published: 1991
Total Pages: 205
ISBN-13: 0821825046
DOWNLOAD EBOOKLet [italic]G be a simple algebraic group of exceptional type over an algebraically closed field of characteristic [italic]p. The subgroups of [italic]G maximal with respect to being closed and connected are determined, although mild restrictions on [italic]p are required in dealing with certain simple subgroups of low rank. For [italic]p = 0 we recover the results of Dynkin.
Author: Alastair J. Litterick
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 168
ISBN-13: 1470428377
DOWNLOAD EBOOKThe study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.
Author: Adam Robert Thomas
Publisher:
Published: 2014
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Martin W. Liebeck
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 122
ISBN-13: 0821804618
DOWNLOAD EBOOKThe theory of simple algebraic groups is important in many areas of mathematics. The authors of this book investigate the subgroups of certain types of simple algebraic groups and obtain a complete description of all those subgroups which are themselves simple. This description is particularly useful in understanding centralizers of subgroups and restrictions of representations.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 242
ISBN-13: 0821834827
DOWNLOAD EBOOKIntends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.