Morita's duality for split reductive groups (Q423611)

The author extends the work in [\textit{Z. Qi} and \textit{C. Yang}, Int. J. Number Theory 7, No. 8, 2115--2137 (2011; Zbl 1235.22022)] to split reductive groups. 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 are constructed and studied.