Residual spectrum of split reductive groups supported in a Borel subgroup under isogenies
Let \(G\) and \(G'\) be almost simple semi-simple split groups. For a central isogeny \(G\) to \(G'\), the authors describe a relationship between the residual spectrum of \(G\) and \(G'\). In this paper, the authors study the residual spectrum of cuspidal support (\(B, \chi\)) and (\(B', \chi'\)), where \(B\) and \(B'\) are Borel subgroups of \(G\) and \(G'\) respectively, and \(\chi\) and \(\chi'\) are unitary characters on the tori contained in \(B\) and \(B'\). If the residual spectrum of a group in a given isogeny class is known, then all residual spectrums of groups in this isogeny class can be obtained by the relationship described by the authors. As indicated in this paper, one can obtain the residual spectrum of Spin\((2n+1)\) by the residual spectrum of SO\((2n+1)\) which is studied in [\textit{H. Kim}, Pac. J. Math. 199, No. 2, 417--455 (2001; Zbl 1047.22016)]. In addition, the authors give Arthur parameters of those residual spectrums.
scientific article; zbMATH DE number 6164101
scientific article