Transcription of Introduction to representation theory
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Introduction to representation theory
Introduction to representation theoryPavel Etingof, Oleg Golberg, Sebastian Hensel,Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena YudovinaJanuary 10, 2011 Contents1 Basic notions of representation What is representation theory ? .. Algebras .. Representations .. Ideals .. Quotients .. Algebras defined by generators and relations .. Examples of algebras .. Quivers .. Lie algebras .. Tensor products .. The tensor algebra .. Hilbert s third problem .. Tensor products and duals of representations of Lie algebras .. Representations ofsl(2) .. Problems on Lie algebras .. 212 General results of representation Subrepresentations in semisimple representations.
made the following observation: take the multiplication table of a finite group Gand turn it into a matrix X G by replacing every entry gof this table by a variable x g . Then the determinant of X G
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