Irreducibility of Disconnected Subgroups of Exceptional Algebraic Groups PDF Download
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Author: Soumaïa Nadia Ghandour
Publisher:
ISBN:
Category :
Languages : en
Pages : 121
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Book Description
Author: Soumaïa Nadia Ghandour
Publisher:
ISBN:
Category :
Languages : en
Pages : 121
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Book Description
Author: Adam R. Thomas
Publisher: American Mathematical Soc.
ISBN: 1470443376
Category : Education
Languages : en
Pages : 191
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Book Description
This 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.
ISBN: 0821824538
Category : Embeddings
Languages : en
Pages : 198
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Book Description
Let [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.
ISBN: 147041046X
Category : Mathematics
Languages : en
Pages : 122
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Book Description
Let 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.
ISBN: 1470414945
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Let 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: Alastair J. Litterick
Publisher: American Mathematical Soc.
ISBN: 1470428377
Category : Mathematics
Languages : en
Pages : 168
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Book Description
The 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: Gary M. Seitz
Publisher: American Mathematical Soc.
ISBN: 0821825046
Category : Mathematics
Languages : en
Pages : 205
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Book Description
Let [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: Adam Robert Thomas
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
ISBN: 0821804618
Category : Mathematics
Languages : en
Pages : 122
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Book Description
The 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.
ISBN: 0821834827
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Intends 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.
