Groups of Exceptional Type, Coxeter Groups and Related Geometries

1. Front Matter

   Pages i-xiv

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2. A Classification of Curtis-Tits Amalgams

   • Rieuwert J. Blok, Corneliu G. Hoffman

   Pages 1-26

3. The Use of Valuations for Classifying Point-Line Geometries

   • Bart De Bruyn

   Pages 27-40

4. An Outline of Polar Spaces: Basics and Advances

   • Ilaria Cardinali

   Pages 41-74

5. Embeddings of Line-Grassmannians of Polar Spaces in Grassmann Varieties

   • I. Cardinali, A. Pasini

   Pages 75-109

6. Generation of Lie Incidence Geometries: A Survey

   • Bruce N. Cooperstein

   Pages 111-121

7. Witt-Type Theorems for Subspaces of Lie Geometries: A Survey

   • Bruce N. Cooperstein

   Pages 123-133

8. Embeddings of Cotriangular Spaces

   • Hans Cuypers, Jos in ’t Panhuis

   Pages 135-145

9. Unipotent Overgroups in Simple Algebraic Groups

   • Iulian I. Simion, Donna M. Testerman

   Pages 147-158

10. The Axes of a Majorana Representation of \(A_{12}\)

    • A. Castillo-Ramirez, A. A. Ivanov

    Pages 159-188

11. GIT Related Problems of the Flag Variety for the Action of a Maximal Torus

    • S. Senthamarai Kannan

    Pages 189-203

12. Characterizations of Trialities of Type \(\mathrm {I}_{\mathsf {id}}\) in Buildings of Type \(\mathsf {D}_4\)

    • Hendrik Van Maldeghem

    Pages 205-216

13. On the Isomorphism Problem for Coxeter Groups and Related Topics

    • Koji Nuida

    Pages 217-238

14. Lectures on Artin Groups and the \(K(\pi ,1)\) Conjecture

    • Luis Paris

    Pages 239-257

15. Algebraic Codes and Geometry of Some Classical Generalized Polygons

    • N. S. Narasimha Sastry

    Pages 259-278

16. Some Weyl Modules of the Algebraic Groups of Type \(E_6\)

    • Peter Sin

    Pages 279-300

17. Back Matter

    Pages 301-304

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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.

• Buekenhout Geometries
• Coxeter Groups
• Groups of Exceptional Type
• Moufang Sets
• Spherical Buildings

• Stat Math Unit, Indian Statistical Institute, Bangalore, India

  N.S. Narasimha Sastry

N.S. NARASIMHA SASTRY is Professor and Head of Department of Mathematics at Indian Statistical Institute, Bengaluru, India. He received his Ph.D.  from University of Pittsburgh, Pennsylvania, USA and has held visiting positions at Tata Institute of Fundamental Research, Mumbai, India;  Michigan State University, East Lansing, USA; University of Western Australia, Perth, Australia; Rutgers University, New Brunswick,  USA; University of Florida, Gainsville, USA and University of Ghent, Belgium. He has served as referee for journals such as Journal of Algebra; Codes, Designs and Cryptography and Journal of Pure and Applied Algebra and has published in journals such as Journal of Algebra, Journal of Combinatorial Theory (Series A), Geometriae Dedicata, Journal of Functional Analysis, Journal of Operator Theory, Proceedings in Indian Academy of Sciences, Journal of Algebraic Combinatorics and Archiv der Mathematik. Some of the books edited by him include Groups, Finite Geometries and Buildings, published by Springer and Essays in Geometric Group Theory, published by the Ramanujam Mathematical Society. He has co-edited Perspectives in Mathematical Sciences, (Volumes 1 and 2), published by World Scientific. His research interests are finite groups including finite simple groups, geometries related to finite simple groups, algebraic codes, Coxeter groups and the Monster.

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