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| 008 | 100301s2008 gw | s |||| 0|eng d | ||
| 020 | _a9783540773993 | ||
| 024 | 7 |
_a10.1007/978-3-540-77399-3 _2doi |
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| 035 | _a978-3-540-77399-3 | ||
| 072 | 7 |
_aPBF _2bicssc |
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| 072 | 7 |
_aMAT002010 _2bisacsh |
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| 082 | 0 | 4 | _a512.44 |
| 090 | _amg | ||
| 100 | 1 |
_aStekolshchik, Rafael _99361 |
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| 245 | 1 | 0 |
_aNotes on Coxeter Transformations and the McKay Correspondence _h[electronic resource]/ _cby Rafael Stekolshchik. |
| 260 |
_aBerlin, Heidelberg: _bSpringer Berlin Heidelberg, _c2008. |
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| 300 | _bdigital. | ||
| 490 | 0 |
_aSpringer Monographs in Mathematics, _x1439-7382 |
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| 505 | 0 | _aIntroduction -- 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 -- A. The McKay correspondence and the Slodowy correspondence -- B. Regularity conditions for representations of quivers -- C. Miscellanea -- References -- Index . | |
| 520 | _aOne 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 |
_aMathematics _943458 |
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| 650 | 0 |
_aAlgebra _943450 |
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| 650 | 0 |
_aGroup theory _943436 |
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| 650 | 0 |
_aTopological groups. _943823 |
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| 697 |
_aMatemáticas Gerais- _x(inclusive alguns textos elementares sobre assuntos específicos) _923752 |
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| 710 | 1 |
_aSpringerLink (Online service). _98857 |
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| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783540773986 |
| 830 | 0 |
_aSpringer monographs in mathematics, _924417 |
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| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-540-77399-3 |
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_2impa _cEBK |
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| 999 |
_aSTEKOLSHCHIK, Rafael. <b> Notes on Coxeter Transformations and the McKay Correspondence. </b> Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. (Springer Monographs in Mathematics, 1439-7382). ISBN 9783540773993. Disponível em: <http://dx.doi.org/10.1007/978-3-540-77399-3 > _c38590 _d38590 |
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