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AuthorKane, Richard. author
TitleReflection Groups and Invariant Theory [electronic resource] / by Richard Kane ; edited by Jonathan Borwein, Peter Borwein
ImprintNew York, NY : Springer New York : Imprint: Springer, 2001
Connect tohttp://dx.doi.org/10.1007/978-1-4757-3542-0
Descript IX, 379 p. online resource

SUMMARY

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


CONTENT

I Reflection groups -- 1 Euclidean reflection groups -- 2 Root systems -- 3 Fundamental systems -- 4 Length -- 5 Parabolic subgroups -- II Coxeter groups -- 6 Reflection groups and Coxeter systems -- 7 Bilinear forms of Coxeter systems -- 8 Classification of Coxeter systems and reflection groups -- III Weyl groups -- 9 Weyl groups -- 10 The Classification of crystallographic root systems -- 11 Affine Weyl groups -- 12 Subroot systems -- 13 Formal identities -- IV Pseudo-reflection groups -- 14 Pseudo-reflections -- 15 Classifications of pseudo-reflection groups -- V Rings of invariants -- 16 The ring of invariants -- 17 Poincarรฉ series -- 18 Nonmodular invariants of pseudo-reflection groups -- 19 Modular invariants of pseudo-reflection groups -- VI Skew invariants -- 20 Skew invariants -- 21 The Jacobian -- 22 The extended ring of invariants -- VII Rings of covariants -- 23 Poincarรฉ series for the ring of covariants -- 24 Representations of pseudo-reflection groups -- 25 Harmonic elements -- 26 Harmonics and reflection groups -- VIII Conjugacy classes -- 27 Involutions -- 28 Elementary equivalences -- 29 Coxeter elements -- 30 Minimal decompositions -- IX Eigenvalues -- 31 Eigenvalues for reflection groups -- 32 Eigenvalues for regular elements -- 33 Ring of invariants and eigenvalues -- 34 Properties of regular elements -- Appendices -- A Rings and modules -- B Group actions and representation theory -- C Quadratic forms -- D Lie algebras -- References


Mathematics Mathematical analysis Analysis (Mathematics) Geometry Mathematics Analysis Geometry



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