Multiplicity-Free Schubert Calculus

[摘要] Multiplicity-free algebraic geometry is the study of subvarieties$Ysubseteq X$ with the ``smallest invariants'' as witnessed by amultiplicity-free Chow ring decomposition of $[Y]in A^{star}(X)$ into a predetermined linear basis. This paper concerns the case of Richardson subvarieties of the Grassmannianin terms of the Schubert basis. We give a nonrecursive combinatorialclassification of multiplicity-free Richardson varieties, i.e.,we classify multiplicity-free products of Schubert classes. This answersa question of W. Fulton.

[学科分类] 数学（综合）

[关键词] generalized Greiner operator;polar coordinates;Hardy inequality