Kraśkiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials

2016/03/19 by Masaki Watanabe, Watanabe, Masaki
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1603.06080

arxiv created 2016/03/19 · openalex publication_date 2016/03/19 · arxiv updated 2016/03/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In their 1987 paper Kraśkiewicz and Pragacz defined certain modules, which we call KP modules, over the upper triangular Lie algebra whose characters are Schubert polynomials. In a previous work the author showed that the tensor product of KP modules always has a KP filtration, i.e. a filtration whose each successive quotients are isomorphic to KP modules. In this paper we explicitly construct such filtrations for certain special cases of these tensor product modules, namely S_w ⊗ S^d(Kⁱ) and S_w ⊗ \bigwedge^d(Kⁱ), corresponding to Pieri and dual Pieri rules for Schubert polynomials.

Citations

• Kraśkiewicz-Pragacz modules and Ringel duality

Cited by

• On a certain family of U(b)-modules

Related

• Tensor product of Kraśkiewicz and Pragacz's modules
• Kraśkiewicz-Pragacz modules and Ringel duality
• An approach toward Schubert positivities of polynomials using Kraśkiewicz-Pragacz modules
• Filtrations and recursions for Schubert modules
• On a certain family of U(b)-modules