The symmetric Macdonald polynomials may be constructed from the nonsymmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their nonsymmetric counterparts. In taking this approach we are able to obtain new results as well as simpler and more accessible derivations of a number of the known fundamental properties of both kinds of polynomials.
- Hecke algebras
- Macdonald polynomials