A geometric Littlewood-Richardson rule

• Autores: Ravi Vakil
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 164, Nº 2, 2006, págs. 371-422
• Idioma: inglés
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• Resumen

  • 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 eld, 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 rst 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.