Algebras and Representations

Part of the Graduate Texts in Mathematics book series (GTM, volume 255)


In this chapter we develop some algebraic tools needed for the general theory of representations and invariants. The central result is a duality theorem for locally regular representations of a reductive algebraic group G. The duality between the irreducible regular representations of G and irreducible representations of the commuting algebra of G plays a fundamental role in classical invariant theory. We study the representations of a finite group through its group algebra and characters, and we construct induced representations and calculate their characters.


Irreducible Representation Conjugacy Class Hopf Algebra Associative Algebra Group Algebra 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSan DiegoUSA

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