Description
Since their introduction by Drinfeld and
Jimbo in 1985 in the
studies of exactly solvable models, quantum
enveloping algebras
have been one of the most important tools
to describe new
symmetries.
For q=0, there is a good base (the so-called
crystal base) of the representation of a
quantum enveloping algebra U_{q}(mathfrak{g})
of a semi-simple Lie algebra mathfrak{g}.
A modified action of root vectors sends the
crystal base to itself, thus providing a
rich combinatorial structure. Therefore one
can reduce many properties of representation
to the combinatorics of crystal bases.
In this book, the author presents crystal
bases and their
applications to multiplicities and weights
of the tensor products
of two representations.
Contents
Representations de l'algebre quantique U_q(mathfrak{sl}_2)
Bases cristallines des U_q(mathfrak{sl}_2)-modules
L'algebre enveloppante quantique U_q(mathfrak{g})
Bases cristallines des U_q(mathfrak{g})-modules
Cas de mathfrak{gl}_n
Bases globales des U_q(mathfrak{g})-modules
Base cristalline B(infty) de l'algebre U^-_q(mathfrak{g})
Realisation des bases cristallines par des
chemins
Cristaux et groupe de Weyl
Bibliographie
Index des notations
Index terminologique
Details:
Series: Cours Specialises--Collection SMF,
Number: 9
Publication Year: 2003
ISBN: 2-85629-126-0
200 p., soft cover, ISBN 3-88538-227-X, 2003
This volume presents a selection of worked-out
lectures that were
held at the 2nd German-Korean Workshop on
Algebra and Topology
which took place at Pusan, Korea, in August
2000. The papers
present surveys and new results primarily
in the fields of Group
Theory and Low-Dimensional Topology that
have not been published
elsewhere.
Contents
Preface vii
P. Ackermann, M. Naatanen, G. Rosenberger
The Arithmetic Fuchsian Groups with Signature
R. Brown, M. Bullejos, T. Porter
Crossed Complexes, Free Crossed Resolutions
and Graph Products of
Groups
C. M. Campbell, P. P. Campbell, B. T. K.
Hopson, E. F. Robertson
On the Efficiency of Direct Powers of PGL(2,
p)
D. A. Derevnin, Ann Chi Kim
The Coxeter Prisms in H3
D. Hennig, G. Rosenberger
Recent Developments in the Theory of Fuchsian
and Kleinian Groups
Ann Chi Kim, Yangkok Kim
On Generalized Whitehead Links and 3-Manifolds
Jae-Ryong Kim, Moo Ha Woo
Topology Fields and Fixed Points of Flows
E. Kudryavtseva, R. Weidmann, H. Zieschang
Quadratic Equations in Free Groups and Topological
Applications
A. Mednykh, A. Vesnin
Colourings of Polyhedra and Hyperelliptic
3-Manifolds
J. Mennicke
Linear Groups over Rings of Integers
Ch. Menzel, J. R. Parker
Pseudo-Anosov Diffeomorphisms of the Twice
Punctured Torus
M. Mulazzani
3-Manifolds with Cyclic Symmetry and (1,1)-Knots
A. Szczepanski
Holonomy Groups of Crystallographic Groups
with Finite Outer
Automorphism Groups
K.-I. Tahara
Survey on Dimension Subgroup Problem
136 p., soft cover, ISBN 3-88538-228-8, 2003
Quaternionic analysis is the most natural
and close
generalization of complex analysis that preserves
many of its
important features. The present book is meant
as an introduction
and invitation to this theory and its applications
(in fact it
was inspired by a course given by the author
to graduate
engineering students). Restricting ourselves
to Maxwell's
equations and the Dirac equation only we
show the progress
achieved in applied quaternionic analysis
during the last five
years, emphasising results which can not
so easily be obtained by
other methods. Thus, the main objective of
this work is to
introduce the reader to some topics of quaternionic
analysis
whose selection is motivated by particular
models from the theory
of electromagnetic and spinor fields, and
to show the usefulness
and necessity of applying the tools of quaternionic
analysis to
these kinds of problems.
This book is an introductory graduate level
text on game theory, which grew out of courses
for students in Mathematics in Nijmegen and
for students in Econometrics and Operations
Research in Tilburg.
Game theory deals with mathematical models
of conflict and
cooperation.
In the first nine chapters attention is paid
to non-cooperative
games in
extensive and strategic form and to some
economic applications.
Relations with the theory of linear programming
and the theory of
linear complementarity are indicated.
In the last ten chapters different types
of cooperative games and
solution
concepts are treated. Economic applications
and applications in
OR-situations with multiple agents are discussed.
A rich collection of exercises, partly with
solutions, is
included.
Contents
1. Introduction
2. Game in Strategic form
3. Two-person zero-sum games
4. Mixed extensions of bimatrix games
5. The Nash equilibria of a 3-person game
6. Linear programming and matrix games
7. Linear complementarity and bimatrix games
8. Potential games
9. Other topics in non-cooperative game theory
10. Games in coalitional form
11. The imputation set and the core
12. Linear production games
13. Dominance, the D-core and stable sets
14. The Shapley value
15. The r-value
16. The nucleolus
17. Bargaining games
18. NTU-games
19. The NTU-value
A Solutions of Exercises
B Extra exercises
Bibliography
Index
Texts and Readings in Mathematics/ 23
March 2003, 184 pages, Hardback, ISBN 81-85931-37-2
This is an elementary introduction to the
congruence subgroup
problem, a problem which deals with number
theoretic properties
of groups defined arithmetically.
The novelty and, indeed, the goal of this
book is to present some
applications to group theory as well as to
number theory which
have emerged in the last fifteen years.
No knowledge of algebraic groups is assumed
and the choice of the
examples discussed seeks to convey that even
these special cases
give interesting applications.
After the background material in group theory
and number theory,
solvable groups are treated first and some
generalisations are
presented using class field theory.Then the
group SL(n) over
rings of S-integers is studied. The methods
involved are very
different from the ones employed
for solvable groups. Group theoretic properties
like
presentations and central extensions are
extensively used.
Several proofs which appeared after the original
ones are
discussed.
The last chapter has a survey of the status
of the congruence
subgroup problem for general algebraic groups.
Only outlines of
proofs are given here and with a sufficient
understanding of
algebraic groups the proofs can be completed.
The book is intended for beginning graduate
students. Many
exercises are given.
Contents
Preface
1. A review of background material
2. Solvable groups
3. SL2 - The negative solutions
4. SLn(Os) - Positive cases of CSP
5. Applications of the CSP
6. CSP in general algebraic groups
Appendix
Bibliography
Index
Texts and Readings in Mathematics/ 24
March 2003, 318 pages, Hardback, ISBN 81-85931-38-0