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Pieri's formula via explicit rational equivalence

  Published:1997-12-01
 Printed: Dec 1997
  • Frank Sottile
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Abstract

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.
Keywords: Pieri's formula, rational equivalence, Grassmannian, Schensted insertion Pieri's formula, rational equivalence, Grassmannian, Schensted insertion
MSC Classifications: 14M15, 05E10 show english descriptions Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Combinatorial aspects of representation theory [See also 20C30]
14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
05E10 - Combinatorial aspects of representation theory [See also 20C30]
 

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