Expected publication date is March 6, 2003
Description
Hecke algebras arise in representation theory as endomorphism
algebras of induced representations. One of the most important
classes of Hecke algebras is related to representations of
reductive algebraic groups over p-adic or finite fields. In 1979,
in the simplest (equal parameter) case of such Hecke algebras,
Kazhdan and Lusztig discovered a particular basis (the KL-basis)
in a Hecke algebra, which is very important in studying relations
between representation theory and geometry of the corresponding
flag varieties. It turned out that the elements of the KL-basis
also possess very interesting combinatorial properties.
In the present book, the author extends the theory of the KL-basis
to a more general class of Hecke algebras, the so-called algebras
with unequal parameters. In particular, he formulates conjectures
describing the properties of Hecke algebras with unequal
parameters and presents examples verifying these conjectures in
particular cases.
Written in the author's precise style, the book gives researchers
and graduate students working in the theory of algebraic groups
and their representations an invaluable insight and a wealth of
new and useful information.
Contents
Coxeter groups
Partial order on W
The algebra {\mathcal H}
The bar operator
The elements c_w
Left or right multiplication by c_s
Dihedral groups
Cells
Cosets of parabolic subgroups
Inversion
The longest element for a finite W
Examples of elements D_w
The function \mathbf{a}
Conjectures
Example: The split case
Example: The quasisplit case
Example: The infinite dihedral case
The ring J
Algebras with trace form
The function {\mathbf{a}}_E
Study of a left cell
Constructible representations
Two-sided cells
Virtual cells
Relative Coxeter groups
Representations
A new realization of Hecke algebras
Bibliography
Other titles in this series
Details:
Series: CRM Monograph Series,Volume: 18
Publication Year: 2003
ISBN: 0-8218-3356-1
Paging: 136 pp.
Binding: Hardcover
Expected publication date is March 2, 2003
Description
The papers presented in this volume are written by participants
of the "Symplectic and Contact Topology, Quantum Cohomology,
and Symplectic Field Theory" symposium. The workshop was
part of a semester-long joint venture of The Fields Institute in
Toronto and the Centre de Recherches Mathematiques in Montreal.
The twelve papers cover the following topics: Symplectic
Topology, the interaction between symplectic and other geometric
structures, and Differential Geometry and Topology.
The Proceeding concludes with two papers that have a more
algebraic character. One is related to the program of Homological
Mirror Symmetry: the author defines a category of extended
complex manifolds and studies its properties. The subject of the
final paper is Non-commutative Symplectic Geometry, in particular
the structure of the symplectomorphism group of a non-commutative
complex plane.
The in-depth articles make this book a useful reference for
graduate students as well as research mathematicians.
Contents
M. Abreu -- Kahler geometry of toric manifolds in symplectic
coordinates
V. Apostolov and T. Draghici -- The curvature and the
integrability of almost-Kahler manifolds: A survey
F. Bourgeois -- A Morse-Bott approach to contact homology
J. Chen -- Deforming surfaces in four dimensional manifolds
A. Dancer and M. Y. Wang -- Integrability and the Einstein
equations
J. Epstein and D. Fuchs -- On the invariants of Legendrian mirror
torus links
R. Ibanez, Yu. Rudyak, A. Tralle, and L. Ugarte -- Symplectically
harmonic cohomology of nilmanifolds
D. Kotschick -- Godbillon-Vey invariants for families of
foliations
S. A. Merkulov -- A note on extended complex manifolds
V. Pidstrygach -- On action of symplectomorphisms of the complex
plane on pairs of matrices
L. Polterovich -- Slow symplectic maps, continued fractions, and
related stories
J.-C. Sikorav -- The gluing construction for normally generic J-holomorphic
curves
Details:
Series: Fields Institute Communications,Volume: 35
Publication Year: 2003
ISBN: 0-8218-3162-3
Paging: approximately 207 pp.
Binding: Hardcover
Description
The aim of this book is to explain modern homotopy theory in a
manner accessible to graduate students yet structured so that
experts can skip over numerous linear developments to quickly
reach the topics of their interest. Homotopy theory arises from
choosing a class of maps, called weak equivalences, and then
passing to the homotopy category by localizing with respect to
the weak equivalences, i.e., by creating a new category in which
the weak equivalences are isomorphisms. Quillen defined a model
category to be a category together with a class of weak
equivalences and additional structure useful for describing the
homotopy category in terms of the original category. This allows
you to make constructions analogous to those used to study the
homotopy theory of topological spaces.
A model category has a class of maps called weak equivalences
plus two other classes of maps, called cofibrations and
fibrations. Quillen's axioms ensure that the homotopy category
exists and that the cofibrations and fibrations have extension
and lifting properties similar to those of cofibration and
fibration maps of topological spaces. During the past several
decades the language of model categories has become standard in
many areas of algebraic topology, and it is increasingly being
used in other fields where homotopy theoretic ideas are becoming
important, including modern algebraic K-theory and algebraic
geometry.
All these subjects and more are discussed in the book, beginning
with the basic definitions and giving complete arguments in order
to make the motivations and proofs accessible to the novice. The
book is intended for graduate students and research
mathematicians working in homotopy theory and related areas.
Contents
Localization of model category structures
Summary of part 1
Local spaces and localization
The localization model category for spaces
Localization of model categories
Existence of left Bousfield localizations
Existence of right Bousfield localizations
Fiberwise localization
Homotopy theory in model categories
Summary of part 2
Model categories
Fibrant and cofibrant approximations
Simplicial model categories
Ordinals, cardinals, and transfinite composition
Cofibrantly generated model categories
Cellular model categories
Proper model categories
The classifying space of a small category
The Reedy model category structure
Cosimplicial and simplicial resolutions
Homotopy function complexes
Homotopy limits in simplicial model categories
Homotopy limits in general model categories
Index
Bibliography
Details:
eries: Mathematical Surveys and Monographs, Volume: 99
Publication Year: 2003
ISBN: 0-8218-3279-4
Paging: 457 pp.
Binding: Hardcover
Expected publication date is March 15, 2003
Description
This book presents articles from the conference on algebraic
coverings held in March 2000 in St. Etienne (France). The goal of
the conference was to introduce the algebraic bases of this
theory and to give a survey of the research tools. These
proceedings reflect the spirit of the conference.
The book includes widely accessible survey and research papers on
a range of topics, including inverse Galois theory, moduli
spaces, problems of descent, rigid geometry, the language of
stacks and gerbs and its applications, Galois modules, and
morphisms of curves. There is also an appendix with a short
lecture on topological and algebraic covers that will make a good
introduction to the subject for the non-specialist.
The volume is intended for advanced graduate students and
researchers. It would make a nice addition to a seminar on
algebraic coverings.
Contents
P. Debes -- Theorie de Galois et geometrie: une introduction
P. Debes -- Methodes topologiques et analytiques en theorie
inverse de Galois: Theoreme d'existence de Riemann
Q. Liu -- Une mini introduction a la geometrie analytique rigide
M. Emsalem -- Espaces de Hurwitz
S. Flon -- Corps des modules et bonnes places
J.-C. Douai -- Descente, champs et gerbes de Hurwitz
Ph. Satge -- Morphismes d'une courbe de genre $2$ vers une courbe
de genre $1$
N. Borne -- Modules galoisiens sur les courbes: une introduction
P. Debes -- Annexe: Revetements topologiques
Details:
Series: Seminaires et Congres, Number: 5
Publication Year: 2002
ISBN: 2-85629-116-3
Paging: 214 pp.
Binding: Softcover