English

Kra\'skiewicz-Pragacz modules and Ringel duality

Representation Theory 2015-11-24 v2 Combinatorics

Abstract

Kra\'skiewicz 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 Kra\'skiewicz-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.

Keywords

Cite

@article{arxiv.1504.04657,
  title  = {Kra\'skiewicz-Pragacz modules and Ringel duality},
  author = {Masaki Watanabe},
  journal= {arXiv preprint arXiv:1504.04657},
  year   = {2015}
}
R2 v1 2026-06-22T09:18:11.040Z