Buch, Englisch, 379 Seiten, Format (B × H): 164 mm x 244 mm, Gewicht: 680 g
Reihe: CMS Books in Mathematics
Buch, Englisch, 379 Seiten, Format (B × H): 164 mm x 244 mm, Gewicht: 680 g
Reihe: CMS Books in Mathematics
ISBN: 978-0-387-98979-2
Verlag: Springer
Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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 Poincaré 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 Poincaré 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.
