Corpus ID: 208857616

On certain sign characters of tori and their extensions to Bruhat-Tits groups

@article{Fintzen2019OnCS,
  title={On certain sign characters of tori and their extensions to Bruhat-Tits groups},
  author={Jessica Fintzen and Tasho Kaletha and Loren Spice},
  journal={arXiv: Representation Theory},
  year={2019}
}
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… Expand
Supercuspidal L-packets
Let F be a non-archimedean local field and let G be a connected reductive group defined over F. We assume that G splits over a tame extension of F and that the residual characteristic p does notExpand

References

SHOWING 1-9 OF 9 REFERENCES
On L-embeddings and double covers of tori over local fields
To every maximal torus T of a connected reductive group G defined over a local field F we associate a canonical double cover of the topological group T(F) of its F-rational points. We furtherExpand
Stability of character sums for positive-depth, supercuspidal representations
We re-write the character formul{\ae} of Adler and the second-named author in a form amenable to explicit computations in $p$-adic harmonic analysis, and use them to prove the stability of characterExpand
Regular supercuspidal representations
We show that, in good residual characteristic, most supercuspidal representations of a tamely ramified reductive p-adic group G arise from pairs (S,\theta), where S is a tame elliptic maximal torusExpand
An Intertwining Result for p-adic Groups
Abstract For a reductive $p$ -adic group $G$ , we compute the supports of the Hecke algebras for the $K$ -types for $G$ lying in a certain frequently-occurring class. When $G$ is classical, weExpand
Topological Jordan decompositions
Abstract The notion of a topological Jordan decomposition of a compact element of a reductive p -adic group has proven useful in many contexts. In this paper, we generalise it to groups defined overExpand
Shelstad, Foundations of twisted endoscopy, Astérisque
  • vi+190. MR
  • 1999
Endomorphisms of linear algebraic groups
, and Scott A . Vanstone , On the number of self - dual bases of GF ( q m ) over GF ( q )
  • J . Reine Angew . Math .