Notes on Coxeter Transformations and the McKay Correspondence

• Main Author: Stekolshchik, Rafael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebra.; Commutative algebra.; Commutative rings.; Group theory.; Topological groups.; Lie groups.; Functional analysis.; Functional Analysis.; Commutative Rings and Algebras.; Topological Groups, Lie Groups.; Group Theory and Generalizations.

One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram. The Coxeter transformation is the main tool in the proof...

Table of Contents:

• Preliminaries
• The Jordan normal form of the Coxeter transformation
• Eigenvalues, splitting formulas and diagrams Tp,q,r
• R. Steinberg’s theorem, B. Kostant’s construction
• The affine Coxeter transformation.