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Notes on Coxeter Transformations and the McKay Correspondence

  • Kartonierter Einband
  • 260 Seiten
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One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between repr... Weiterlesen
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Beschreibung

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.



Includes a number of new proofs relating to Coxeter Transformations and the McKay Correspondence

Ideas and formulae from a wide variety of researchers in the field



Autorentext

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.



Inhalt
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.

Produktinformationen

Titel: Notes on Coxeter Transformations and the McKay Correspondence
Autor:
EAN: 9783642096044
ISBN: 3642096042
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Anzahl Seiten: 260
Gewicht: 400g
Größe: H235mm x B155mm x T14mm
Jahr: 2010
Auflage: Softcover reprint of hardcover 1st ed. 2008

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