Annals of Combinatorics 1 (1997) 367-375

Multiplication of a Schubert Polynomial by a Schur Polynomial

Axel Kohnert

Lehrstuhl Mathematik II, Universität Bayreuth, 95440 Bayreuth, Germany

Received August 14, 1997

AMS Subject Classification: 05E05, 14M15

Abstract. Schur polynomials are a special case of Schubert polynomials. In this paper, we give an algorithm to compute the product of a Schubert polynomial with a Schur polynomial on the basis of Schubert polynomials. This is a special case of the general problem of the multiplication of two Schubert polynomials, where the corresponding algorithm is still missing. The main tools for the given algorithm is a factorization property of a special class of Schubert polynomials and the transition formula for Schubert polynomials.

Keywords: Schubert polynomial, Schur function, transition formula


1.  N. Bergeron and S. Billey, RC-graphs and Schubert polynomials, Experimental Mathematics 2 (1993) 257–269.

2.  S. Fomin and A.N. Kirillov, The Young-Baxter equation, symmetric functions and Schubert polynomials, Discrete Math. 153 (1996) 123–143.

3.  A. Kohnert, Weintrauben, Polynome, Tableaux, Bayreuther Mathematische Schriften 38 (1990) 1–97.

4.  A. Kohnert, Schubert polynomials and skew Schur functions, J. Symbolic Computation 14 (1992) 205–210.

5.  A. Lascoux and M.P. Schützenberger, Classes de Chern des Variété de drapeaux, C.R. Acad. Sc. Paris 294 (1982)393–398.

6.  A. Lascoux and M.P. Schützenberger, Schubert polynomials and the LIttlewood-Richardson rule, Letters in Mathematical Physics 10 (1985) 11–124.

7.  D.Mouk, Geometry of flag manifolds, Proc. London Math. Soc. (3) 9 (1959) 253–286.

Get the LaTex | DVI | PS file of this abstract.