Buildings, Finite Geometries and Groups: Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010 ... (Springer Proceedings in Mathematics (10))

This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas. Front Matter....Pages i-xii On Characterizing Designs by Their Codes....Pages 1-14 The Geometry of Extremal Elements in a Lie Algebra....Pages 15-35 Properties of a 27-Dimensional Space of Symmetric Bilinear Forms Acted on by E 6 ....Pages 37-47 On the Geometry of Global Function Fields, the Riemann–Roch Theorem, and Finiteness Properties of S -Arithmetic Groups....Pages 49-80 Some Remarks on Two-Transitive Permutation Groups as Multiplication Groups of Quasigroups....Pages 81-91 Curve Complexes Versus Tits Buildings: Structures and Applications....Pages 93-152 On Isotypies Between Galois Conjugate Blocks....Pages 153-162 Representations of Unitriangular Groups....Pages 163-174 Hermitian Veronesean Caps....Pages 175-191 On a Class of c . F 4 -Geometries....Pages 193-230 Buildings and Kac-Moody Groups....Pages 231-250 Some Equations Over Finite Fields Related to Simple Groups of Suzuki and Ree Types....Pages 251-271 Oppositeness in Buildings and Simple Modules for Finite Groups of Lie Type....Pages 273-286 Modular Representations, Old and New....Pages 287-304 The Use of Blocking Sets in Galois Geometries and in Related Research Areas....Pages 305-327 Quadratic Action....Pages 329-336 Back Matter....Pages 337-341 This volume collects articles inspired by the Proceedings of the ICM 2010 Satellite Conference on "Buildings, Finite Geometries and Groups" organized at the Indian Statistical Institute, Bangalore, from August 29 - 31, 2010. These contributors include some of the most active researchers in areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, and more. Contributions reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective that the authors bring to their articles on current developments and major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these fields Annotation These articles reflect the current major trends in research in the geometric and combinatorial aspects of study of finite simple groups, Chevalley groups and their generalisations.