Notes on Coxeter Transformations and the McKay Correspondence

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Stekolshchik, Rafael (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Edición:1st ed. 2008.
Colección:Springer Monographs in Mathematics,
Temas:
Algebra.
Functional analysis.
Commutative algebra.
Commutative rings.
Topological groups.
Lie groups.
Group theory.
Functional Analysis.
Commutative Rings and Algebras.
Topological Groups and Lie Groups.
Group Theory and Generalizations.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Notes on Coxeter Transformations and the McKay Correspondence  |h [electronic resource] /  |c by Rafael Stekolshchik. 
250 |a 1st ed. 2008. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2008. 
300 |a XX, 240 p. 28 illus.  |b online resource. 
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505 0 |a 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. 
520 |a 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. 
650 0 |a Algebra. 
650 0 |a Functional analysis. 
650 0 |a Commutative algebra. 
650 0 |a Commutative rings. 
650 0 |a Topological groups. 
650 0 |a Lie groups. 
650 0 |a Group theory. 
650 1 4 |a Algebra. 
650 2 4 |a Functional Analysis. 
650 2 4 |a Commutative Rings and Algebras. 
650 2 4 |a Topological Groups and Lie Groups. 
650 2 4 |a Group Theory and Generalizations. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783642096044 
776 0 8 |i Printed edition:  |z 9783540846796 
776 0 8 |i Printed edition:  |z 9783540773986 
830 0 |a Springer Monographs in Mathematics,  |x 2196-9922 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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