Moritaʼs duality for split reductive groups

In this paper, we extend the work in [Z. Qi, C. Yang, Moritaʼs theory for the symplectic groups, Int. J. Number Theory 7 (2011) 2115–2137 [7]] to split reductive groups. We construct and study the holomorphic discrete series representations and the principal series representations of a split reductive group G over a p-adic field F as well as a duality between certain sub-representations of these two representations.