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