Krakenkiewicz-Pragacz模与Ringel对偶
Kraśkiewicz-Pragacz modules and Ringel duality
摘要：
Krakenkiewicz和Pragacz介绍了以舒伯特多项式为特征的上三角李代数的表示。在以前的工作中，作者利用最高权范畴理论研究了Krakiewicz-Pragacz模的结构。特别地，从那里的结果，我们得到了一个最高权范畴，它的标准模是KP模。在本文中，我们证明了这个最高权范畴是自Ringel对偶的：这导致了一个有趣的对称关系之间的KP模的Ext群。我们还证明了b-模上的张量积运算与Ringel对偶函子是相容的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
