Schubert and Macdonald Polynomials , a parallel

  title={Schubert and Macdonald Polynomials , a parallel},
  author={Alain Lascoux},
Schubert and (non-symmetric) Macdonald polynomials are two linear bases of the ring of polynomials which can be characterized by vanishing conditions. We show that both families satisfy similar branching rules related to the multiplication by a single variable. These rules are sufficient to recover a great part of the theory of Schubert and Macdonald polynomials.