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Pieri’S Formula Via Explicit Rational Equivalence

Published online by Cambridge University Press:  20 November 2018

Frank Sottile
Frank Sottile*
Affiliation:
Department of Mathematics University of Toronto 100 St. George Street Toronto, Ontario
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Abstract

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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

14M1505E10Pieri’s formularational equivalenceGrassmannianSchensted insertion
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 6 , 01 December 1997 , pp. 1281 - 1298
Copyright
Copyright © Canadian Mathematical Society 1997

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