Skew Divided Difference Operators and Schubert Polynomials

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2007
• Main Author: Kirillov, A.N.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147361
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Skew Divided Difference Operators and Schubert Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 12 назв. — англ.

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the...