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MAT 5327

Topics in Algebra

3 units

Winter 2022 · Symmetric Functions

Topics

  • Partitions, tableaux and graded rings
  • Symmetric polynomials and symmetric functions
  • Elementary, complete and power-sum bases
  • Schur functions and the Hall inner product
  • Hopf algebra structure
  • Characters and representations of symmetric groups
  • Bosonic and fermionic Fock spaces; boson–fermion correspondence

Readings

  • Symmetric Functions and Hall Polynomials
    I. G. Macdonald · Optional additional reference
  • An Introduction to Symmetric Functions and Their Combinatorics
    E. S. Egge · Optional additional reference
  • Introduction to Symmetric Functions
    M. Zabrocki · Optional additional reference
  • Symmetric Functions: lecture notes ↗
    Main course reference
Sources