2 edition of On representations of finite groups with split BN-pairs found in the catalog.
On representations of finite groups with split BN-pairs
Ahmed A. Khammash
Thesis (Ph.D.) - University of Warwick, 1987.
|Statement||Ahmed A. Khammash.|
Split BN-Pairs of Rank at Least 2 and the Uniqueness of Splittings The 2-Modular Reduction of the Steinberg Representation of a Finite Chevalley Group of Type C n On the Restrictions of Modular Irreducible Representations of Algebraic Groups of Type A . Howlett RB: Normalizers of parabolic subgroups of reflection groups. Journal of the London Mathematical Society, Second Series, 21 (), 62– MR80b C1. Howlett RB and Kilmoyer RW: Principal series representations of finite groups with split \(BN\) pairs. Communications in Algebra, 8 (), – MR81d C1.
The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing. The sporadic finite simple groups aren't that big! The Monster group is smaller than the alternating group on 50 letters. I think a better place for you to start (rather than wondering about general intuition for very particular objects) would be to look at Griess's Twelve Sporadic freelancerscomic.com recollection is that that book is quite accessible, and it'll let you get a glimpse of what's going on.
Khukhro, E. I. () Finite groups admitting a Frobenius group of automorphisms with fixed-point-free kernel. In: Fourth groupo Theory Conference of Iran, March , Isfahan, Iran. Khukhro, E. I. () Finite groups and Lie rings admitting a Frobenius group of automorphisms with fixed-point-free kernel. Khammash, Ahmed A. () On representations of finite groups with split BN-pairs. PhD thesis, University of Warwick. Klippenstein, John () Applications of the universal coefficient theorem for connective K-theory. PhD thesis, University of Warwick. Klimowicz, Anthony Aleksander () Fitting and formation theory in locally finite groups.
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Oct 12, · This cohomological approach carries over to the context of algebraic groups in characteristic p.
In essence, this is where the book Modular Representations of Finite Groups of Lie Type begins. After a brief introduction, Humphreys guides the reader through the some of the major theorems and conjectures in the subject.
Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved.
This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
Khammash, Ahmed A. () On representations of finite groups with split BN-pairs. PhD thesis, University of Warwick. Finite Groups with a Split BN-pair of Rank 1. 1* CHRISTOPH HERING AND WILLIAM M. KANTOR Department of Mathematics, University of Illinois, Chicago, Illinois AND GARY M.
SEITZ Department of Mathematics, University of Oregon, Eugene, Oregon TO PROFESSOR RICHARD BRAUER, TO COMMEMORATE HIS SEVENTIETH BIRTHDAY, FEBRUARY 10, Received Cited by: In mathematics, a reductive group is a type of linear algebraic group over a freelancerscomic.com definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation with finite kernel which is a direct sum of irreducible freelancerscomic.comive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of.
Mar 15, · 1. Split BN-pairs of Tits rank 1 for groups of finite Morley rank Here we collect some facts concerning the definability and connectivity of certain subgroups of oups of finite Morley rank with a split BN-pair of Tits rank 1.
oposition Cited by: 3. Abstract. Since all finite simple groups have been classified , it is a natural question whether the major conjectures in modular representation theory are consequences of this important and deep classification freelancerscomic.com this article, a survey is given about the progress which has been achieved on the famous open conjectures of J.
Alperin  and R. Brauer  during the last freelancerscomic.com by: 5. Modular representations of finite monoids of Lie type Modular representations of finite monoids of Lie type Renner, Lex Let M be a finite monoid of Lie type of characteristic p.
In this paper we compute the number of irreducible modular representations of M in characteristic freelancerscomic.com: Renner, Lex. Darstellungstheoretische Methoden bei der Realisierung einfacher Gruppen vom Lie Typ als Galoisgruppen.
Representations of reductive groups over finite fields, Ann. of Math. (), Multiplicities of principal series representations of finite groups with split BN-pairs, J.
Cited by: 9. Jul 04, · 6. Borel, Properties and linear representations of Chevalley groups, Part A, Seminar on Algebraic Groups and Related Finite Groups, Lecture Notes in Math., vol. Springer-Verlag, Berlin and New York, Cited by: Some irreducible characters of groups with BN pairs, PhD thesis, University of Adelaide ().
L3: Some irreducible characters of groups with BN pairs, Journal of Algebra 39 () – MR 54 # L4: Principal series representations of finite groups with split BN pairs, Communications in Algebra 8 () – (Co-author R.
The Levi decomposition of a split (B,N)-pair Modular Representations of Split BN Pairs. Article. proof of a key technical result in the theory of modular Lie representations of finite. Characters of finite groups of Lie type.
II ; Principal series representations of finite groups with split (BN)-pairs ; Cartan invariants and decomposition numbers of Chevalley groups ; Duality in the character ring of a finite Chevalley group ; Characters of projective indecomposable modules for finite Chevalley.
New simple groups with a BN-pair. June ; This completes the classification of split BN-pairs of rank 2, generalizing the corresponding result for finite groups due to Fong and Seitz.
As a consequence one gets for example the Harish-Chandra theory for irreducible ordinary representations of finite groups of Lie type as special case.
Secondly we extend the classical theory of vertices and sources to Hecke algebras associated with Coxeter freelancerscomic.com by: 1. VARIOUS CONSTRUCTIONS FOR FINITE GROUPS OF LIE TYPE FINITE REDUCTIVE GROUPS BN-PAIRS FINITE GROUPS OF LIE TYPE AND THEIR REPRESENTATIONS – LECTURE I Gerhard Hiss Lehrstuhl D für Mathematik RWTH Aachen University Groups St Andrews in Bath University of Bath, August 1 – 15, In Gorenstein (, Appendix) announced a program for completing the classification of finite simple groups, consisting of the following 16 steps: Groups of low 2-rank.
This was essentially done by Gorenstein and Harada, who classified the groups with sectional 2-rank at most 4. FINITE GROUPS OF LIE TYPE AND THEIR REPRESENTA-TIONS GERHARD HISS Lehrstuhl D fur¨ Mathematik, RWTH Aachen University, Aachen, Germany Email: [email protected] This article is a slightly expanded account of the series of four lectures I gave at the conference.
It is intended as a (non-comprehensive) survey covering some. You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.
Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Oct 31, · The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series.
This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important freelancerscomic.comon: Rutgers University, New Brunswick, NJ. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material.
An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups.Jan 01, · Split BN-Pairs of Rank at Least 2 and the Uniqueness of Splittings The 2-Modular Reduction of the Steinberg Representation of a Finite Chevalley Group of Type On the Restrictions of Modular Irreducible Representations of Algebraic Groups of Type to Cited by: 8.We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable stabilisers of points.