An approach toward Schubert positivities of polynomials using Kraśkiewicz-Pragacz modules

2014/06/24 by Masaki Watanabe, Watanabe, Masaki · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1406.6203

added explanations; corrected a mistake in the proof of Proposition 6.4

arxiv created 2015/07/03 · arxiv updated 2015/07/06

Abstract

In this paper, we investigate properties of modules introduced by Kraśkiewicz and Pragacz which realize Schubert polynomials as their characters. In particular, we give some characterizations of modules having a filtration by Kraśkiewicz-Pragacz modules. In finding criteria for filtrations, we calculate generating sets for the annihilator ideals of the lowest vectors in Kraśkiewicz-Pragacz modules, and derive a projectivity result concerning Kraśkiewicz-Pragacz modules.

Cited by

• Kraśkiewicz-Pragacz modules and Ringel duality
• On a certain family of U(b)-modules

Related

• Tensor product of Kraśkiewicz and Pragacz's modules
• Kraśkiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials
• On a certain family of U(b)-modules
• Filtrations and recursions for Schubert modules
• Kraśkiewicz-Pragacz modules and Ringel duality