Séminaire Lotharingien de Combinatoire, B50i (2004), 32 pp.

Alain Lascoux

SCHUBERT & GROTHENDIECK: Un bilan bidécennal

English Abstract. We give a dozen formulas concerning Schubert and Grothendieck polynomials, and their interrelations, half of them being new, and most of them interesting. In particular, we describe explicitly the decomposition of Schubert polynomials as positive sums of Grothendieck polynomials, and we show that non-commutative Schubert polynomials are obtained by reading the columns of a two-dimensional Cauchy kernel. A six pages summary in English has been added.

Received: June 1, 2004. Accepted: November 10, 2004. Final Version: December 21, 2004.

The following versions are available: