Pieri's rule for flag manifolds and Schubert polynomials release_hn5r2lm4jnhtpghnvpcpwxcaoe

by Frank Sottile

Released as a article .

1995  

Abstract

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary symmetric polynomial or a complete homogeneous symmetric polynomial. Thus, we generalize the classical Pieri's rule for symmetric polynomials/Grassmann varieties to Schubert polynomials/flag manifolds. Our primary technique is an explicit geometric description of certain intersections of Schubert varieties. This method allows us to compute additional structure constants for the cohomology ring, which we express in terms of paths in the Bruhat order on the symmetric group.
In text/plain format

Archived Files and Locations

application/pdf  249.5 kB
file_p7l2b6dvyzbuxdtz6sxnc5juji
archive.org (archive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   1995-05-02
Version   v1
Language   en ?
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 19bd2a9a-0578-4234-b7b0-f9c053dbff00
API URL: JSON