Symmetric Functions

• Introduction to Symmetric Functions

• Symmetric Functions

• Symmetric functions, with their multiple realizations

• Classical symmetric functions

• Schur symmetric functions

• Monomial symmetric functions

• Multiplicative symmetric functions

• Elementary symmetric functions

• Homogeneous symmetric functions

• Power sum symmetric functions

• Characters of the symmetric group as bases of the symmetric functions

• Orthogonal Symmetric Functions

• Symplectic Symmetric Functions

• Generic dual bases symmetric functions

• Symmetric functions defined by orthogonality and triangularity

• Kostka-Foulkes Polynomials

• Hall-Littlewood Polynomials

• Hecke Character Basis

• Jack Symmetric Functions

• k-Schur Functions

• Quotient of symmetric function space by ideal generated by Hall-Littlewood symmetric functions

• LLT symmetric functions

• Macdonald Polynomials

• Non-symmetric Macdonald Polynomials

• Witt symmetric functions