Morita始s duality for split reductive groups

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• 作者：Zhi Qi ^{qi@math.ohio-state.edu}
• 关键词：Split reductive groups ; Principal series representations ; Rigid analytic symmetric space ; Holomorphic discrete series representations ; Duality
• 刊名：Journal of Number Theory
• 出版年：2012
• 期刊代码：78_0022314x
• 类别：mt
• 出版时间：August, 2012
• 卷：132
• 期：8
• 页码：1664-1685
• 文件大小：283 K

摘要

In this paper, we extend the work in [Z. Qi, C. Yang, Morita始s theory for the symplectic groups, Int. J. Number Theory 7 (2011) 2115-2137 ] 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.