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MAT 4199

Special Topics in Mathematics

3 units

Fall 2017 · Modern Group Theory

Topics

  • Finite-group representations, characters and tensor products
  • Group algebras and Frobenius reciprocity
  • Branching rules and Gelfand–Tsetlin bases
  • Partitions and Young tableaux
  • Jucys–Murphy elements
  • Okounkov–Vershik approach to symmetric-group representations

Readings

  • Representation Theory of the Symmetric Groups
    Ceccherini-Silberstein; Scarabotti; Tolli · 2010 · Optional; followed closely for parts of the course
  • Linear and Projective Representations of Symmetric Groups
    Kleshchev · 2009 · Optional advanced reference
  • Py. On the representation theory of the symmetric groups. Journal of Mathematical Sciences 129(2), 2005.
  • MAT5145-Modern group theory ↗
    Lecture notes / supplementary course reference
Sources