The Reductive Subgroups of F4 is popular PDF and ePub book, written by David I. Stewart in 2013, it is a fantastic choice for those who relish reading online the Categories genre. Let's immerse ourselves in this engaging Categories book by exploring the summary and details provided below. Remember, The Reductive Subgroups of F4 can be Read Online from any device for your convenience.
The Reductive Subgroups of F4 Book PDF Summary
Let G=G(K) be a simple algebraic group defined over an algebraically closed field K of characteristic p ≥ 0. A subgroup X of G is said to be G-completely reducible if, whenever it is contained in a parabolic subgroup of G, it is contained in a Levi subgroup of that parabolic. A subgroup X of G is said to be G-irreducible if X is in no proper parabolic subgroup of G; and G-reducible if it is in some proper parabolic of G. In this paper, we consider the case that G = F4(K). We find all conjugacy classes of closed, connected, semisimple G-reducible subgroups X of G. Thus we also find all non-G-completely reducible closed, connected, semisimple subgroups of G. When X is closed, connected and simple of rank at least two, we find all conjugacy classes of G-irreducible subgroups X of G. Together with the work of Amende classifying irreducible subgroups of type A1 this gives a complete classification of the simple subgroups of G. Amongst the classification of subgroups G=F4(K) we find infinite varieties of subgroups X of G which are maximal amongst all reductive subgroups of G but not maximal subgroups of G; thus they are not contained in any reductive maximal subgroup of G. The connected, semisimple subgroups contained in no maximal reductive subgroup of G are of type A1 when p=3 and of type A21 or A1 when p = 2. Some of those which occur when p=2 act indecomposably on the 26-dimensional irreducible representation of G. We also use this classification to find all subgroups of G=F4 which are generated by short root elements of G, by utilising and extending the results of Leibeck and Seitz.
Detail Book of The Reductive Subgroups of F4 PDF
- Author : David I. Stewart
- Release : 02 July 2024
- Publisher : Unknown
- ISBN : 0821898736
- Genre : Categories
- Total Page : 88 pages
- Language : English
- PDF File Size : 19,6 Mb
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