Abstract
Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. This paper solves the long standing open problem of giving a non-iterative formula for straightening a filling. We apply our formula to give a complete generalization of a theorem of Gonciulea and Lakshmibai.
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Acknowledgements
The author would like to thank Venkatramani Lakshmibai and Alexander Yong for helpful discussions, comments, and suggestions. The author would also like to thank the anonymous referee for suggestions that significantly simplified the main argument and improved the overall clarity.
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