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Introduction to representation theory

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Introduction to representation theoryPavel Etingof, Oleg Golberg, Sebastian Hensel,Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena YudovinaJanuary 10, 2011Contents1 Basic notions of representation What is representation theory ? . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . Quotients.

group algebra A= C[G] of a finite group G– the algebra with basis ag,g∈ Gand multiplication law agah = agh. We will show that any finite dimensional representation of Ais a direct sum of irreducible representations, i.e., the notions of an irreducible and indecomposable representation are the same for A(Maschke’s theorem).

  Group, Representation

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