Groups of Exceptional Type, Coxeter Groups and Related Geometries

✍ Scribed by N.S. Narasimha Sastry (eds.)

• Publisher: Springer India
• Year: 2014
• Tongue: English
• Leaves: 311
• Series: Springer Proceedings in Mathematics & Statistics 82
• Edition: 1
• Category: Library

✦ Synopsis

The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.

✦ Table of Contents

Front Matter....Pages i-xiv
A Classification of Curtis-Tits Amalgams....Pages 1-26
The Use of Valuations for Classifying Point-Line Geometries....Pages 27-40
An Outline of Polar Spaces: Basics and Advances....Pages 41-74
Embeddings of Line-Grassmannians of Polar Spaces in Grassmann Varieties....Pages 75-109
Generation of Lie Incidence Geometries: A Survey....Pages 111-121
Witt-Type Theorems for Subspaces of Lie Geometries: A Survey....Pages 123-133
Embeddings of Cotriangular Spaces....Pages 135-145
Unipotent Overgroups in Simple Algebraic Groups....Pages 147-158
The Axes of a Majorana Representation of $$A_{12}$$ ....Pages 159-188
GIT Related Problems of the Flag Variety for the Action of a Maximal Torus....Pages 189-203
Characterizations of Trialities of Type $$\mathrm {I}_{\mathsf {id}}$$ in Buildings of Type $$\mathsf {D}_4$$ ....Pages 205-216
On the Isomorphism Problem for Coxeter Groups and Related Topics....Pages 217-238
Lectures on Artin Groups and the $$K(\pi ,1)$$ Conjecture....Pages 239-257
Algebraic Codes and Geometry of Some Classical Generalized Polygons....Pages 259-278
Some Weyl Modules of the Algebraic Groups of Type $$E_6$$ ....Pages 279-300
Back Matter....Pages 301-304

✦ Subjects

Group Theory and Generalizations; Algebraic Geometry; Geometry