Classification of strongly positive representations of even general unitary groups (Q2283641)

Strongly positive representations can be viewed as the basic building blocks for the discrete series in the case of classical groups, after the work of \textit{C. Moeglin} [J. Eur. Math. Soc. (JEMS) 4, No. 2, 143--200 (2002; Zbl 1002.22009)] and \textit{C. Moeglin} and \textit{M. Tadić} [J. Am. Math. Soc. 15, No. 3, 715--786 (2002; Zbl 0992.22015)]. In this article, following the arguments in the work [\textit{I. Matić}, J. Algebra 334, No. 1, 255--274 (2011; Zbl 1254.22010)] and the appendix to [\textit{Y. Kim}, Math. Z. 279, No. 1--2, 271--296 (2015; Zbl 1319.22013) ] of the second-named author, the authors give a classification of strongly positive (discrete series) representations of even unitary groups and even general unitary groups over a \( p \)-adic field \( F \) of characteristic different from \( 2 \). Classification of strongly positive representations of even unitary groups has also been done by Mœglin and Tadić using a different approach in [\textit{C. Moeglin} and \textit{M. Tadić}, J. Am. Math. Soc. 15, No. 3, 715--786 (2002; Zbl 0992.22015)]. The approach in the article under review is based on the Tadić structure formula which describes the explicit structure of the Jacquet modules of parabolically induced representations. They obtain the Tadić structure formula for these two classes of groups in Sections 3 and 5 respectively. For the entire collection see [Zbl 1414.11004].