Beta extensions and cuspidal types for \(p\)-adic spin groups
Let \(F\) be a non-Archimedean local field of characteristic zero with odd residual characteristic. Let \(\hat{G}\) be a spin group over \(F\). The author constructs a large class of supercuspidal representations of \(\hat{G}\). He comments that, in some cases, the exhaustion of the construction has been proved in his thesis. This paper uses the semisimple type method developed by Bushnell and Kutzko when constructing supercuspidal representations of \(GL(n)\). Then, using this method, Stevens in a series of papers and \textit{M. Miyauchi} and \textit{S. Stevens} [Math. Ann. 358, No. 1--2, 257--288 (2014; Zbl 1294.22015)] constructed supercuspidal representations of \(p\)-adic classical groups, \textit{L. Blasco} and \textit{C. Blondel} [Ann. Sci. Éc. Norm. Supér. (4) 45, No. 6, 985--1025 (2012; Zbl 1271.22014)] studied the case of the exceptional group \(G_2\). Note that recently much progress has been made on the construction of supercuspidal representations using Bruhat-Tits building theory. It is an interesting and important question how these two kinds of construction are explicitly connected with each other.
construction of supercuspidal representations
scientific article; zbMATH DE number 6690955
scientific article