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}
}