Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is detailed account of this interplay.
In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Because of the connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.
Introduction
1 Preliminaries 2 Structure Theory of Semisimple Rings 3. Representation Theory of Finite Groups 4 Representation Theory of the Symmetric Group 5 Symmetric Polynomials 6 Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C) 7 Structure Theory of Complex Semisimple Lie Algebras 8 Representation Theory of Complex Semisimple Lie Algebras 9 Generalities on Algebraic Groups 10 Structure Theory of Reductive Groups 11 Representation Theory of Semisimple Algebraic Groups 12 Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory 13 Singular Locus of a Schubert Variety in the Flag Variety SLn/B 14 Applications. Appendix: Chevalley Groups.
Bibliography.
List of Symbols.
Index.
Text and Readings in Mathematics/ 53
2009 288 pages Hardcover ISBN 81-85931-92-0
Collection Methodes
ISBN : 978 2 7056 6797 9
Nombre de pages : 240 / Format : 15 x 22 cm
Le mouvement desordonne de particules de pollen en suspension dans un liquide en equilibre
fut observe et rigoureusement rapporte par le botaniste ecossais Robert Brown en 1827.
Ce phenomene aleatoire lie a l’agitation moleculaire recut par la suite le nom de mouvement
brownien. Sa description mathematique comme un processus stochastique a captive
l’attention des physiciens et mathematiciens depuis plus d’un siecle. Il intervient dans de tres
nombreux modeles en physique, chimie, biologie, sciences economiques et mathematiques
financieres.
Le mouvement brownien est l’objet central du calcul des probabilites moderne : il est tout a la
fois une martingale, un processus gaussien, un processus a accroissements independants et un
processus de Markov. Ces diverses proprietes qui en font le processus stochastique par
excellence, sont presentees dans cet ouvrage avec les deux outils qu’il permet de developper :
l’integrale d’Ito et la notion d’equation differentielle stochastique.
Ce livre s’adresse a tous ceux et celles qui recherchent une introduction rapide et rigoureuse
aux methodes du calcul stochastique, en particulier aux etudiants des master de
mathematiques, aux eleves des grandes ecoles scientifiques ainsi qu’aux candidats a
l’agregation. Nous y avons inclus des exercices de difficulte variee, corriges en fin de volume,
pour en faciliter la lecture et l’utilisation comme outil pedagogique.
Auteur :
Leonard Gallardo est professeur a l’universite de Tours.
ISBN: 978-0-470-14832-7
Paperback
360 pages
April 2009
The second edition of Statistical Control by Monitoring and Adjustment,
with revised and expanded chapters, is an updated version of a classic
text in the field of quality control. Practice exercises with solutions,
detailed explanations of key concepts, and a clear presentation with numerous
examples and computational tables demonstrate how to improve industrial
efficiency by combining statistical and engineering process quality control.
This book, which provides feedback methods that can be of immediate use,
is ideal for graduate students studying quality control and professional
quality control engineers and statisticians.
Preface.
Chapter 1: Introduction and Statistics Revision.
Chapter 2: Standard Control Charts: A First Approximation.
Chapter 3: What Can Go Wrong and What Can We Do About It?
Chapter 4: Introduction to Forecasting and Process Dynamics.
Chapter 5: Non-Stationary Time Series Models for Process Disturbances.
Chapter 6: Repeated Feedback Adjustment.
Chapter 7: Periodic Adjustment.
Chapter 8: Control of a Process with Inertia.
Chapter 9: Explicit Consideration of Monetary Cost.
Chapter 10: Cuscore Charts: Looking for Signals in Noise.
Chapter 11: Monitoring an Operating Feedback System.
Chapter 12: A Brief Review of Time Series Analysis.
Bibliography and Further Reading.
ISBN: 978-0-471-49657-1
Hardcover
400 pages
June 2009
Decision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice.
The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives.
Provides a rich collection of techniques and procedures.
Discusses the foundational aspects and modern day practice.
Links foundations to practical applications in biostatistics, computer science, engineering and economics.
Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics.
Decision Theory is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book.
ISBN: 978-0-470-51792-5
Hardcover
416 pages
May 2009
Statistical and Methodological Aspects of Oral Health Research provides oral health researchers with an overview of the methodological aspects that are important in planning, conducting and analyzing their research projects whilst also providing biostatisticians with an idea of the statistical problems that arise when tackling oral health research questions.
This collection presents critical reflections on oral health research and offers advice on practical aspects of setting up research whilst introducing the reader to basic as well as advanced statistical methodology.
An introduction to research methodology and an exposition of the state of the art.
A variety of examples from oral health research.
Contributions from well-known oral health researchers, epidemiologists and biostatisticians, all of whom have rich experience in this area.
Recent developments in statistical methodology prompted by a variety of dental applications.
Presenting both an introduction to research methodology and an exposition of the latest advances in oral health research, this book will appeal both beginning and experienced oral health researchers as well as biostatisticians and epidemiologists.