Expected publication date is December 28,
2003
Description
Now back in print by the AMS, this is a significantly
revised edition of a book originally published
in 1987 by Academic Press. This book gives
the reader an introduction to the theory
of algebraic representations of reductive
algebraic groups. To develop appropriate
techniques, the first part of the book is
an introduction to the general theory of
representations of algebraic group schemes.
Here, the author describes important basic
notions: induction functors, cohomology,
quotients, Frobenius kernels, and reduction
mod p, among others.
The second part of the book is devoted to
the representation
theory of reductive algebraic groups. It
includes topics such as
the description of simple modules, vanishing
theorems, the Borel-Bott-Weil
theorem and Weyl's character formula, and
Schubert schemes and
line bundles on them.
For this revised edition the author added
nearly 150 pages of new
material describing some later developments,
among them Schur
algebras, Lusztig's conjecture and Kazhdan-Lusztig
polynomials,
tilting modules, and representations of quantum
groups. He also
made major revisions to parts of the old
text.
Jantzen's book continues to be the ultimate
source of information
on representations of algebraic groups in
finite characteristics.
It is suitable for graduate students and
research mathematicians
interested in algebraic groups and their
representations.
Contents
Part I. General theory
Schemes
Group schemes and representations
Induction and injective modules
Cohomology
Quotients and associated sheaves
Factor groups
Algebras of distributions
Representations of finite algebraic groups
Representations of Frobenius kernels
Reduction mod p
Part II. Representations of reductive groups
Reductive groups
Simple G-modules
Irreducible representations of the Frobenius
kernels
Kempf's vanishing theorem
The Borel-Bott-Weil theorem and Weyl's character
formula
The linkage principle
The translation functors
Filtrations of Weyl modules
Representations of G_rT and G_rB
Geometric reductivity and other applications
of the Steinberg
modules
Injective G_r-modules
Cohomology of the Frobenius kernels
Schubert schemes
Line bundles on Schubert schemes
Truncated categories and Schur algebras
Results over the integers
Lusztig's conjecture and some consequences
Radical filtrations and Kazhdan-Lusztig polynomials
Tilting modules
Frobenius splitting
Frobenius splitting and good filtrations
Representations of quantum groups
References
List of notations
Index
Details:
Series: Mathematical Surveys and Monographs,
Volume: 107
Publication Year: 2003
ISBN: 0-8218-3527-0
Paging: 576 pp.
Binding: Hardcover
Expected publication date is December 28,
2003
Description
The volume includes lecture notes and research
papers by
participants of the Seventh Symposium on
Probability and
Stochastic Processes held in Mexico City.
The lecture notes
introduce recent advances in stochastic calculus
with respect to
fractional Brownian motion, principles of
large deviations and of
minimum entropy concerning equilibrium prices
in random economic
systems, and give a complete and thorough
survey of credit risk
theory.
The research papers cover areas such as financial
markets,
Gaussian processes, stochastic differential
equations, stochastic
integration, quantum dynamical semigroups,
self-intersection
local times, etc.
Readers should have a basic background in
probability theory,
stochastic integration, and stochastic differential
equations.
The book is suitable for graduate students
and research
mathematicians interested in probability,
stochastic processes,
and risk theory.
This volume is a joint publication of the
American Mathematical
Society and the Sociedad Matematica Mexicana.
Contents
Lecture notes
D. Nualart -- Stochastic integration with
respect to fractional
Brownian motion and applications
E. Nummelin -- Entropy and economic equilibrium
T. Schmidt and W. Stute -- Credit risk-A
survey
Research papers
N. Castaneda-Leyva and D. Hernandez-Hernandez
-- Optimal
investment in incomplete financial markets
with stochastic
volatility
M. Galea, J. Ma, and S. Torres -- Price calculation
for power
exponential jump-diffusion models--A Hermite-series
approach
J. C. Garcia and R. Quezada -- Conditions
for nonconservativity
in quantum dynamical semigroups
J. M. Gonzalez-Barrios -- Some notes on a
dependency measure
J. Gonzalez-Hernandez -- An example of an
averaged Markov
decision process without stable policies
E. Gordienko, M. Mendieta, and J. Ruiz de
Chavez -- Closeness
estimates for sums of independent random
variables
C. Houdre and J. Villa -- An example of infinite
dimensional
quasi-helix
J. A. Leon and M. Sarra -- A non-homogeneous
wave equation driven
by a Poisson process
J. A. Lopez-Mimbela and J. Villa -- Existence
of self-intersection
local time of the multitype Dawson-Watanabe
superprocess
V. Perez-Abreu and A. Rocha-Arteaga -- Levy
processes in Banach
spaces: Distributional properties and subordination
L. A. Rincon -- Phase space path integral
representation for the
solution of a stochastic Schrodinger equation
A. Talarczyk -- A note on covariance characterization
of some
generalized Gaussian random fields
C. Tudor -- On two-parameter Stieltjes integrals
for functions in
Besov-Liouville spaces and stochastic integrals
Details:
Series: Contemporary Mathematics, Volume:
336
Publication Year: 2003
ISBN: 0-8218-3466-5
Paging: 272 pp.
Binding: Softcover
Expected publication date is January 8, 2004
Description
This extraordinary volume contains a large
part of the
mathematical correspondence between A. Grothendieck
and J-P.
Serre. It forms a vivid introduction to the
development of
algebraic geometry during the years 1955-1965.
During this
period, algebraic geometry went through a
remarkable
transformation, and Grothendieck and Serre
were among central
figures in this process.
In the book, the reader can follow the creation
of some of the
most important notions of modern mathematics.
The letters also
reflect the mathematical and political atmosphere
of this period.
They are supplemented by J-P. Serre's notes,
which give
explanations, corrections, and references
to further results.
The book is a unique bilingual (French and
English) volume. The
original French text is supplemented here
by the English
translation, with French text printed on
the left-hand pages and
the corresponding English text printed on
the right. The book
also includes several facsimiles of original
letters. The
original French volume was edited by Pierre
Colmez and J-P. Serre.
The English translation for this volume was
prepared by Catriona
Maclean with the assistance of Leila Schneps
and J-P. Serre.
The book should be useful to specialists
in algebraic geometry,
mathematical historians, and to all mathematicians
who want to
experience the unfolding of great mathematics.
Contents
P. Colmez and J.-P. Serre -- Correspondence
Notes
Bibliography
Details:
Publication Year: 2003
ISBN: 0-8218-3424-X
Paging: approximately 592 pp.
Binding: Hardcover
Expected publication date is January 4, 2004
Description
Starting in the late 1950's, Kolmogorov,
Arnold, and Moser
developed a theory (now known as the KAM
theory) for the study of
persistence of quasiperiodic motion in mechanical
systems.
By now, this is a full-fledged theory, which
has proved to be
fundamental in the study of long term behavior
in dynamics (ergodic
theory and topological stability) and its
applications (plasma
physics, celestial mechanics, etc.). It has
also grown into a
very important tool for many problems in
functional analysis and
its applications. This unique text examines
and compares various
approaches to KAM theory and surveys its
relationship to other
mathematical disciplines.
This book presents in a systematic way the
prerequisites for
reading the original literature, compares
different approaches,
and explains why the approaches work.
The many exercises and examples allow the
reader to work out
important aspects of the theory. It is well-suited
for
independent study or for a graduate course
on ergodic theory and
dynamics.
Contents
Some motivating examples
Preliminaries
Two KAM proofs in a model problem
Hard implicit function theorems
Persistence of invariant tori for quasi-integrable
systems
Aubry-Mather theory
Some remarks on computer assisted proofs
Some recent developments
Bibliography
Details:
Series: University Lecture Series, Volume:
32
Publication Year: 2004
ISBN: 0-8218-3532-7
Paging: approximately 176 pp.
Binding: Softcover
Expected publication date is January 4, 2004
Description
An entirely new branch of science now known
as Laser Control of
Molecular Processes is steadily making an
impact on the
experimental and technological worlds, with
internationally
distinguished scientists making many outstanding
contributions.
In parallel, mathematicians from control
theory and numerical
simulation are getting progressively involved
and making their
contributions to this scientific endeavor.
This volume presents the proceedings of the
workshop, "Quantum
Control: Mathematical and Numerical Challenges",
held at the
Centre de recherches mathematiques of the
Universite de Montreal
(CRM). The workshop concentrated on advanced
numerical methods
and new mathematical control and optimization
approaches and
tools for the quantum control of matter at
the molecular level
using current laser technology. It brought
together
mathematicians, theoretical chemists, and
physicists working in
the area of control and optimization of systems
to address the
outstanding numerical and mathematical problems.
The volume is suitable for graduate students
and research
mathematicians interested in mathematical
methods of control of
molecular processes. It will also be useful
to chemical engineers
and chemists working in control and optimization
of systems.
Contents
O. Atabek and C. M. Dion -- Molecular alignment
and orientation:
From laser-induced mechanisms to optimal
control
A. Auger, A. Ben Haj-Yedder, and M. Schoenauer
-- Overview and
software guide of evolutionary algorithms;
A case study in
quantum control
A. D. Bandrauk, F. Legare, and H. T. Yu --
Laser control of
molecular states--Nonperturbative examples
V. S. Batista and P. Brumer -- Coherent control:
Principles and
semiclassical implementations
G. Chen, D. A. Church, B.-G. Englert, and
M. S. Zubairy --
Mathematical models of contemporary elementary
quantum computing
devices
M. C. Delfour -- Addendum and remarks on
doubly conservative
numerical schemes for the nonlinear Schrodinger
equation and its
control
R. Illner, H. Lange, and H. Teismann -- A
note on the exact
internal control of nonlinear Schrodinger
equations
C. Le Bris, Y. Maday, and G. Turinici --
Towards efficient
numerical approaches for quantum control
H. Lefebvre-Brion -- Multichannel quantum
defect study of the
control in the frequency domain: Example
of HI
Y. Ohtsuki and H. Rabitz -- Development of
solution algorithms
for quantum optimal control equations in
product spaces
X.-G. Wang and T. Carrington, Jr. -- Using
contracted basis
functions to solve the Schrodinger equation
E. Zuazua -- Remarks on the controllability
of the Schrodinger
equation
Details:
Series: CRM Proceedings & Lecture Notes,
Volume: 33
Publication Year: 2003
ISBN: 0-8218-3330-8
Paging: 211 pp.
Binding: Softcover