Logo - springer
Slogan - springer

Mathematics - Analysis | Reflection Groups and Invariant Theory

Reflection Groups and Invariant Theory

Kane, Richard

2001, IX, 379 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$69.99

(net) price for USA

ISBN 978-1-4757-3542-0

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$94.00

(net) price for USA

ISBN 978-0-387-98979-2

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$94.00

(net) price for USA

ISBN 978-1-4419-3194-8

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

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 Level » Graduate

Keywords » Algebraic topology - Eigenvalue - algebra - minimum - representation theory

Related subjects » Analysis - Geometry & Topology

Table of contents 

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.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Analysis.