2015/04/17 by Masaki Watanabe, Watanabe, Masaki · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.CO #math.RT
paper · pdf · doi:10.48550/arxiv.1504.04657
openalex publication_date 2015/04/17 · arxiv created 2015/11/23 · arxiv updated 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kraśkiewicz and Pragacz introduced representations of the upper-triangular Lie algebras whose characters are Schubert polynomials. In a previous work the author studied the structure of Kraśkiewicz-Pragacz modules using the theory of highest weight categories. From the results there, in particular we obtain a certain highest weight category whose standard modules are KP modules. In this paper we show that this highest weight category is self Ringel-dual: this leads to an interesting symmetry relation on Ext groups between KP modules. We also show that the tensor product operation on b-modules is compatible with Ringel duality functor.