Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (6 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the author
1980 - 1991, CAM (Center of Automation and Metrology), Academy of Sciences of Moldova, Project leader of experimental data processing.
Research and development of programs and mathematical tools for Academy of Sciences of Moldova,
999 – 2007, ECI Telecom (Electronics Corporation of Israel), Israel, Project leader in the Network Management department.
Research and development of algorithmes in the field of Communications and Big Systems.
Bibliographic Information
Book Title: Notes on Coxeter Transformations and the McKay Correspondence
Authors: Rafael Stekolshchik
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-540-77399-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Hardcover ISBN: 978-3-540-77398-6Published: 11 February 2008
Softcover ISBN: 978-3-642-09604-4Published: 30 November 2010
eBook ISBN: 978-3-540-77399-3Published: 18 January 2008
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XX, 240
Number of Illustrations: 28 b/w illustrations
Topics: Algebra, Functional Analysis, Commutative Rings and Algebras, Topological Groups, Lie Groups, Group Theory and Generalizations