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Multiplicity-Free Schubert Calculus

Published online by Cambridge University Press:  20 November 2018

Hugh Thomas  and
Alexander Yong
Hugh Thomas
Affiliation:
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3 e-mail: hugh@math.unb.ca
Alexander Yong
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA e-mail: ayong@illinois.edu
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Abstract

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Multiplicity-free algebraic geometry is the study of subvarieties $Y\,\subseteq \,X$ with the “smallest invariants” as witnessed by a multiplicity-free Chow ring decomposition of $\left[ Y \right]\,\in \,{{A}^{*}}\left( X \right)$ into a predetermined linear basis.

This paper concerns the case of Richardson subvarieties of the Grassmannian in terms of the Schubert basis. We give a nonrecursive combinatorial classification of multiplicity-free Richardson varieties, i.e., we classify multiplicity-free products of Schubert classes. This answers a question of W. Fulton.

Keywords

14M1514M0505E99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 1 , 01 March 2010 , pp. 171 - 186
Copyright
Copyright © Canadian Mathematical Society 2010

References

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