Irreducible Almost Simple Subgroups Of Classical Algebraic Groups
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| Author | : Timothy C. Burness |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 122 |
| Release | : 2015-06-26 |
| Genre | : Mathematics |
| ISBN | : 147041046X |
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. |
| Total Pages | : 100 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470414945 |
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 | : Peter B. Kleidman |
| Publisher | : Cambridge University Press |
| Total Pages | : 317 |
| Release | : 1990-04-26 |
| Genre | : Mathematics |
| ISBN | : 052135949X |
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.
| Author | : Tetsu Mizumachi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 110 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 1470414244 |
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.
| Author | : Hongzi Cong |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 100 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470416573 |
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 .
| Author | : M. Escobedo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 120 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 1470414341 |
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.
| Author | : Ian R. Porteous |
| Publisher | : Cambridge University Press |
| Total Pages | : 309 |
| Release | : 1995-10-05 |
| Genre | : Mathematics |
| ISBN | : 0521551773 |
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.
| Author | : Kieran G. O'Grady |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 188 |
| Release | : 2016-03-10 |
| Genre | : Mathematics |
| ISBN | : 1470416964 |
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.
| Author | : Michael Skeide |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 138 |
| Release | : 2016-03-10 |
| Genre | : Mathematics |
| ISBN | : 1470417383 |
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.
| Author | : Vassilios Gregoriades |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 102 |
| Release | : 2016-03-10 |
| Genre | : Mathematics |
| ISBN | : 1470415631 |
The author studies the equivalence classes under Δ11 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of Δ11-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.
