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Group theory --- Reflection groups.

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Coxeter groups --- Reflection groups --- Groupes de Coxeter --- Coxeter's groups --- Real reflection groups --- Reflection groups, Real --- Coxeter groups. --- Reflection groups. --- 512.81 --- 512.81 Lie groups --- Lie groups --- Finite groups --- Transformations (Mathematics) --- Group theory --- #KOPO:Prof. R. Holvoet

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Coxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them. These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings. This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry.

Coxeter groups. --- Geometric group theory. --- Coxeter's groups --- Real reflection groups --- Reflection groups, Real --- Group theory --- Geometric group theory --- Coxeter groups

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This monograph provides a comprehensive introduction to the Kazhdan-Lusztig theory of cells in the broader context of the unequal parameter case. Serving as a useful reference, the present volume offers a synthesis of significant advances made since Lusztig’s seminal work on the subject was published in 2002. The focus lies on the combinatorics of the partition into cells for general Coxeter groups, with special attention given to induction methods, cellular maps and the role of Lusztig's conjectures. Using only algebraic and combinatorial methods, the author carefully develops proofs, discusses open conjectures, and presents recent research, including a chapter on the action of the cactus group. Kazhdan-Lusztig Cells with Unequal Parameters will appeal to graduate students and researchers interested in related subject areas, such as Lie theory, representation theory, and combinatorics of Coxeter groups. Useful examples and various exercises make this book suitable for self-study and use alongside lecture courses.

Mathematics. --- Group theory. --- Group Theory and Generalizations. --- Hecke algebras. --- Coxeter groups. --- Representations of algebras. --- Algebra --- Coxeter's groups --- Real reflection groups --- Reflection groups, Real --- Group theory --- Algebras, Hecke --- Group algebras --- Groups, Theory of --- Substitutions (Mathematics)

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Reflection Groups and their invariant theory provide the main themes of this book and the first two parts focus on these topics. The first 13 chapters deal with reflection groups (Coxeter groups and Weyl groups) in Euclidean Space while the next thirteen chapters study the invariant theory of pseudo-reflection groups. The third part of the book studies conjugacy classes of the elements in reflection and pseudo-reflection groups. The book has evolved from various graduate courses given by the author over the past 10 years. It is intended to be a graduate text, accessible to students with a basic background in algebra. Richard Kane is a professor of mathematics at the University of Western Ontario. His research interests are algebra and algebraic topology. Professor Kane is a former President of the Canadian Mathematical Society.

Group theory --- Reflection groups --- Invariants --- Mathematical analysis. --- Analysis (Mathematics). --- Geometry. --- Analysis. --- Mathematics --- Euclid's Elements --- 517.1 Mathematical analysis --- Mathematical analysis