On certain supercuspidal representations of symplectic groups associated with tamely ramified extensions : the formal degree conjecture and the root number conjecture

Abstract

The formal degree conjecture and the root number conjecture are verified with respect to supercuspidal representations of $S{p}_{2n}(F)$ and $L$-parameters associated with tamely ramified extension $K/F$ of degree $2n$. The supercuspidal representation is constructed as a compact induction from an irreducible unitary representation of the hyper special compact group $S{p}_{2n}(O_F)$, which is explicitly constructed, based upon the general theory developed by the author, by $K$ and certain character $\theta$ of the multiplicative group $K^{\times }$. $L$-parameter is constructed by the data $\{K,\theta \}$ by means of the local Langlands correspondence of tori and Langlands-Schelstad procedure.

60 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2109.04642

References in corpus (2)

• On the construction of tame supercuspidal representations
• Formal Degree of Regular Supercuspidals