Kraśkiewicz-Pragacz modules and Ringel duality

Masaki Watanabe

Published 2015-04-17Version 1

Kra\'skiewicz and Pragacz introduced representations of the upper-triangular Lie algebras whose characters are Schubert polynomials. In previous works 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, and shows that the tensor product operation on $\mathfrak{b}$-modules is compatible with Ringel duality functor.