1997/05/12 by Nantel Bergeron, Bergeron, Nantel, Frank Sottile +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 05E15 #Secondary 14M15 #alg-geom #math.AG #msc:05E15 #msc:14M15
paper · pdf · doi:10.48550/arxiv.alg-geom/9705013
11 pages, Latex2e, 7 figures, uses epsf.sty. Summary of alg-geom/9703001 for an audience of combinatorialists. To appear in conference abstracts of FPSAC'97 (Formal Power Series and Algebraic Combinatorics, Vienna, July, 1997)
arxiv created 1997/05/12 · arxiv updated 2009/11/30
We use geometry to prove a number of new identities among the Littlewood-Richardson coefficients for Schubert polynomials (Schubert classes in a flag manifold). For many of these identities, there is a companion result about the Bruhat order which should imply the identity, were it known how to express these coefficients in terms of the Bruhat order. This analysis leads the determination of many of these constants. We conclude with an outline of geometric proofs for these identities.