Very cuspidal representations of \(p\)-adic symplectic groups (Q1270106)

Let \(n\geq 2\) be a natural number and \(F\) a non-Archimedean local field. In [Ann. Sci. Éc. Norm. Supér., IV. Sér. 17, 191-225 (1984; Zbl 0549.22009)], \textit{H. Carayol} introduced the notion of very cuspidal representations of open compact subgroups of \(\text{GL}_n(F)\) and proved that, by induction, such representations give supercuspidal representations of \(\text{GL}_n(F)\). This result plays an important role in the determination of the admissible dual of \(\text{GL}_n(F)\) by \textit{C. Bushnell} and \textit{P. Kutzko} [The admissible dual of \(\text{GL}(N)\) via compact open subgroups, Ann. Math. Studies. 129 (Princeton 1993; Zbl 0787.22016)]. In the paper under consideration, the result of Carayol is transferred to the next important case of the group \(\text{Sp}_{2n}(F)\). Supercuspidal representations are constructed via compact induction and their formal degrees are computed.