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| Author | : Maria Chlouveraki |
| Publisher | : Springer |
| Total Pages | : 173 |
| Release | : 2009-08-29 |
| Genre | : Mathematics |
| ISBN | : 3642030645 |
This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory. It can also serve as an introduction to the Hecke algebras of complex reflection groups.
| Author | : Maria Chlouveraki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 173 |
| Release | : 2009-09-14 |
| Genre | : Mathematics |
| ISBN | : 3642030637 |
The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups. This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.
| Author | : David Eisenbud |
| Publisher | : Cambridge University Press |
| Total Pages | : 463 |
| Release | : 2015-11-19 |
| Genre | : Mathematics |
| ISBN | : 1107065623 |
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.
| Author | : Meinolf Geck |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 410 |
| Release | : 2011-05-18 |
| Genre | : Mathematics |
| ISBN | : 0857297163 |
The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
| Author | : Meinolf Geck |
| Publisher | : Cambridge University Press |
| Total Pages | : 405 |
| Release | : 2020-02-27 |
| Genre | : Mathematics |
| ISBN | : 1108489621 |
A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.
| Author | : Hans Schoutens |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 215 |
| Release | : 2010-07-31 |
| Genre | : Mathematics |
| ISBN | : 3642133673 |
Exploring ultraproducts of Noetherian local rings from an algebraic perspective, this volume illustrates the many ways they can be used in commutative algebra. The text includes an introduction to tight closure in characteristic zero, a survey of flatness criteria, and more.
| Author | : Areski Cousin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2011-06-29 |
| Genre | : Mathematics |
| ISBN | : 3642146597 |
The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.
| Author | : Christian Pötzsche |
| Publisher | : Springer |
| Total Pages | : 422 |
| Release | : 2010-08-24 |
| Genre | : Mathematics |
| ISBN | : 3642142583 |
Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.
| Author | : Harry Yserentant |
| Publisher | : Springer |
| Total Pages | : 194 |
| Release | : 2010-05-19 |
| Genre | : Mathematics |
| ISBN | : 3642122485 |
The electronic Schrodi ̈ nger equation describes the motion of N electrons under Coulomb interaction forces in a eld of clamped nuclei. Solutions of this equation depend on 3N variables, three spatial dimensions for each electron. Approxim- ing the solutions is thus inordinately challenging, and it is conventionally believed that a reduction to simpli ed models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to c- vince the reader that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The present notes arose from lectures that I gave in Berlin during the academic year 2008/09 to introduce beginning graduate students of mathematics into this subject. They are kept on an intermediate level that should be accessible to an audience of this kind as well as to physicists and theoretical chemists with a c- responding mathematical training.
| Author | : Nessim Sibony |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 357 |
| Release | : 2010-07-31 |
| Genre | : Mathematics |
| ISBN | : 3642131700 |
The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.
