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PMATH 445

Representations of Finite Groups

Undergraduate

Winter 2025

Topics

  • Calendar description: Basic definitions and examples: subrepresentations and irreducible representations, tensor products of representations. Character theory. Representations as modules over the group ring, Artin–Wedderburn structure theorem for semisimple rings. Induced representations, Frobenius reciprocity, Mackey’s irreducibility criterion.
  • We will cover the above topics (not necessarily in that order) and additional ones as time per- mits. Applications to other areas of math, such as number theory and arithmetic geometry, will be discussed.

Readings

  • James and Liebeck, Representations and Characters of Groups , Cambridge University Press, 2001.
    unspecified
  • Serre, Linear Representations of Finite Groups , Springer, 1977. Digital copy available for free through the UW library (login required).
    unspecified
Sources