Mathematics 697SG - ST-SymFunctions&RepThry/SymGr

Representation theory of the symmetric group can be approached using general theory of group representations or with symmetric functions. This area goes back to foundational work of Frobenius, Schur and Yong and a new approach from Okounkov and Vershik. This course will cover representation theory of the symmetric group using these two approaches. The course will also cover the ring of symmetric functions and its relation to the representation theory of the symmetric group and its applications to enumeration. Topics will include the Littlewood-Richardson rule, formulas for characters, and Schur-Weyl duality.

Prerequisites include undergraduate level Abstract Algebra (Math 411) and either Discrete Mathematics (Math 455) or Combinatorics (Math 513 / ComSci 575).