Pieri's formula via explicit rational equivalence

http://dx.doi.org/10.4153/CJM-1997-063-7
Canad. J. Math. 49(1997), 1281-1298

  Published:1997-12-01
 Printed: Dec 1997

Pieri's formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian. We present a new geometric proof, exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cycles to the intersection of a Schubert cycle with a special Schubert cycle. The geometry of these rational equivalences indicates a link to a combinatorial proof of Pieri's formula using Schensted insertion.