A non-iterative formula for straightening fillings of Young diagrams

Reuven Hodges ^[1]
1. [1] University of Kansas
  
  University of Kansas
  
  City of Lawrence, Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-20
Idioma: inglés
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Resumen
- 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.