Generic Smooth Representations
Alexandre PyvovarovMorningside Center of Mathematics, No. 55 Zhongguancun Donglu, Academy of Mathematics and Systems Science, Beijing, Haidian District, 100190 China
Let be a non-archimedean local field. In this paper we explore genericity of irreducible smooth representations of by restriction to a maximal compact subgroup of . Let be a Bushnell-Kutzko type for a Bernstein component . The work of Schneider-Zink gives an irreducible -representation , which appears with multiplicity one in . Let be an irreducible smooth representation of in . We will prove that is generic if and only if is contained in , in which case it occurs with multiplicity one.
Cite this article
Alexandre Pyvovarov, Generic Smooth Representations. Doc. Math. 25 (2020), pp. 2473–2485DOI 10.4171/DM/804