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