On a certain family of U(b)-modules

2016/03/01 by Piotr Pragacz, Pragacz, Piotr
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1603.00189

22 pages; v3: a reference added, the picture properly located

openalex publication_date 2016/03/01 · arxiv created 2016/10/08 · arxiv updated 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We report on results of Kraśkiewicz and the author, and Watanabe on KP modules materializing Schubert polynomials, and filtrations having KP modules as their subquotients. We discuss applications of KP filtrations and ample KP bundles to positivity, due respectively to Watanabe and Fulton. The article corresponds to the talk given by the author at the conference "IMPANGA 15" in April 2015.

Citations

• Kraśkiewicz-Pragacz modules and Ringel duality
• Kraśkiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials
• An approach toward Schubert positivities of polynomials using Kraśkiewicz-Pragacz modules

Related

• An approach toward Schubert positivities of polynomials using Kraśkiewicz-Pragacz modules
• Tensor product of Kraśkiewicz and Pragacz's modules
• Kraśkiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials
• Filtrations and recursions for Schubert modules
• On the V-filtration of D-modules