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Irreducible Almost Simple Subgroups of Classical Algebraic Groups

Irreducible Almost Simple Subgroups of Classical Algebraic Groups PDF Author: Timothy C. Burness
Publisher: American Mathematical Soc.
ISBN: 147041046X
Category : Mathematics
Languages : en
Pages : 122

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.

Irreducible Almost Simple Subgroups of Classical Algebraic Groups

Irreducible Almost Simple Subgroups of Classical Algebraic Groups PDF Author: Timothy C. Burness
Publisher: American Mathematical Soc.
ISBN: 147041046X
Category : Mathematics
Languages : en
Pages : 122

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.

Irreducible Geometric Subgroups of Classical Algebraic Groups

Irreducible Geometric Subgroups of Classical Algebraic Groups PDF Author: Timothy C. Burness,
Publisher: American Mathematical Soc.
ISBN: 1470414945
Category : Mathematics
Languages : en
Pages : 100

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 .

The Subgroup Structure of the Finite Classical Groups

The Subgroup Structure of the Finite Classical Groups PDF Author: Peter B. Kleidman
Publisher: Cambridge University Press
ISBN: 052135949X
Category : Mathematics
Languages : en
Pages : 317

Book Description
With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras PDF Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
ISBN: 0821869205
Category : Mathematics
Languages : en
Pages : 394

Book Description
This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.

Clifford Algebras and the Classical Groups

Clifford Algebras and the Classical Groups PDF Author: Ian R. Porteous
Publisher: Cambridge University Press
ISBN: 0521551773
Category : Mathematics
Languages : en
Pages : 309

Book Description
The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G(subscript 2), and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

Stability of Line Solitons for the KP-II Equation in $\mathbb {R}^2$

Stability of Line Solitons for the KP-II Equation in $\mathbb {R}^2$ PDF Author: Tetsu Mizumachi
Publisher: American Mathematical Soc.
ISBN: 1470414244
Category : Mathematics
Languages : en
Pages : 110

Book Description
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as . He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward . The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.

Stability of KAM Tori for Nonlinear Schrödinger Equation

Stability of KAM Tori for Nonlinear Schrödinger Equation PDF Author: Hongzi Cong
Publisher: American Mathematical Soc.
ISBN: 1470416573
Category : Mathematics
Languages : en
Pages : 100

Book Description
The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger equation subject to Dirichlet boundary conditions , where is a real Fourier multiplier. More precisely, they show that, for a typical Fourier multiplier , any solution with the initial datum in the -neighborhood of a KAM torus still stays in the -neighborhood of the KAM torus for a polynomial long time such as for any given with , where is a constant depending on and as .

On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation

On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation PDF Author: M. Escobedo
Publisher: American Mathematical Soc.
ISBN: 1470414341
Category : Mathematics
Languages : en
Pages : 120

Book Description
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

Moduli of Double EPW-Sextics

Moduli of Double EPW-Sextics PDF Author: Kieran G. O'Grady
Publisher: American Mathematical Soc.
ISBN: 1470416964
Category : Mathematics
Languages : en
Pages : 188

Book Description
The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.

Classification of $E_0$-Semigroups by Product Systems

Classification of $E_0$-Semigroups by Product Systems PDF Author: Michael Skeide
Publisher: American Mathematical Soc.
ISBN: 1470417383
Category : Mathematics
Languages : en
Pages : 138

Book Description
In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
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