Korman, Jonathan On the local constancy of characters. (English) Zbl 1071.22023 J. Lie Theory 15, No. 2, 561-573 (2005). Let \(F\) be a non-Archimedean local field of characteristic zero and let \(G\) be a connected reductive algebraic group defined over \(F\). Let \(\pi\) be an irreducible admissible representation of \(G(F)\). Then Harish-Chandra defined the character \(\Theta_\pi\) of \(\pi\) as a distribution and showed that it is represented by a locally integrable function which is locally constant on the regular elements of \(G(F)\). In this paper the author develops an alternative approach to these questions, due to R. Howe, to make explicit what “locally constant” means, i.e. for any point of \(G(F)\) he gives a neighbourhood of that point on which \(\Theta_\pi\) is constant. Reviewer: Samuel James Patterson (Göttingen) Cited in 1 Document MSC: 22E50 Representations of Lie and linear algebraic groups over local fields 22E35 Analysis on \(p\)-adic Lie groups 20G25 Linear algebraic groups over local fields and their integers Keywords:characters; reductive \(p\)-adic groups; Bruhat-Tits buildings; Moy-Prasad lattices PDFBibTeX XMLCite \textit{J. Korman}, J. Lie Theory 15, No. 2, 561--573 (2005; Zbl 1071.22023) Full Text: arXiv EuDML Link