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 of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincaré series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.
On these pages, the ideas and formulas due to J. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, H.S.M. Coxeter, V. Dlab and C.M. Ringel, V. Kac, J. McKay, T.A. Springer, B. Kostant, P. Slodowy, R. Steinberg, W. Ebeling and several other authors, as well as the author and his colleagues from Subbotin's seminar, are presented in detail. Several proofs seem to be new.
| ISBN: | 9783540773986 |
| Publication date: | 11th February 2008 |
| Author: | R Stekolshchik |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Hardback |
| Pagination: | 239 pages |
| Series: | Springer Monographs in Mathematics |
| Genres: |
Algebra Functional analysis and transforms Groups and group theory |
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 of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincaré series.
Notes on Coxeter Transformations and the McKay Correspondence features in the following genres: Algebra, Functional analysis and transforms, Groups and group theory
Hardback. Not Available.
Notes on Coxeter Transformations and the McKay Correspondence was written by R Stekolshchik and published by Springer an imprint of Springer Berlin Heidelberg
Notes on Coxeter Transformations and the McKay Correspondence has 239 pages
Yes it is part of Springer Monographs in Mathematics series