Geodesic
A geometric Littlewood–Richardson rule
Ravi Vakil1
1 Department of Mathematics, Stanford University, Stanford, CA 94305, United States
Annals of mathematics, Tome 164 (2006) no. 2, pp. 371-422.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are $1$; this is important for applications. This rule should be seen as a generalization of Pieri’s rule to arbitrary Schubert classes, by way of explicit homotopies. It has straightforward bijections to other Littlewood-Richardson rules, such as tableaux, and Knutson and Tao’s puzzles. This gives the first geometric proof and interpretation of the Littlewood-Richardson rule. Geometric consequences are described here and in [V2], [KV1], [KV2], [V3]. For example, the rule also has an interpretation in $K$-theory, suggested by Buch, which gives an extension of puzzles to $K$-theory.
DOI : 10.4007/annals.2006.164.371

Ravi Vakil 1

1 Department of Mathematics, Stanford University, Stanford, CA 94305, United States 
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Ravi Vakil. A geometric Littlewood–Richardson rule. Annals of mathematics, Tome 164 (2006) no. 2, pp. 371-422. doi : 10.4007/annals.2006.164.371. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.371/

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