A geometric Littlewood-Richardson rule
By Ravi Vakil. 2003
110 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a9e57847d624d910cc8f926c1fa2b48a7fff71b6
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
In Mathematical Physics
Citations in the corpus
- A Littlewood–Richardson rule for two-step flag varieties (2009, background): “For example, there are Littlewood–Richardson rules in terms of Young tableaux [9], puzzles [15], and checkers [18].”
- Flag arrangements and triangulations of products of simplices (2006, background): “We follow [12,41] in representing it as follows:”