On certain sign characters of tori and their extensions to Bruhat-Tits groups
arXiv:1912.03286
Abstract
We consider two sign characters defined on a tamely ramified maximal torus T of a twisted Levi subgroup M of a reductive p-adic group G. We show that their product extends to the stabilizer M(F)_x of any point x in the Bruhat-Tits building of T, and give a formula for this extension. This result is used in the passage between zero and positive depth in the explicit construction of supercuspidal L-packets, as well as in forthcoming work on the Harish-Chandra character formula for supercuspidal representations.
arXiv commentThis paper has been superseded by arXiv:2106.09120, where the material appears in an improved form together with applications