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An analogue of Γ-function for irreducible cuspidal representations of the group GL(2) over a two-dimensional local field
Abstract
Let F be a non-archimedian local field of odd residue characteristic, 𝒪=F[ [t] ]⊂𝒦=F( (t) ). We consider the subgroup GL̂(2,𝒪)=𝒦×·GL(2,𝒪)⊂GL(2,𝒦), and the normalizer GL'(2,𝒪)⊂GL(2,𝒦) of an Iwahori subgroup I⊂GL(2,𝒦). We calculate the Γ-functions for irreducible special representations of GL̂(2,𝒪) and GL'(2,𝒪).
Related
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- The structure of irreducible cuspidal eta quotients
- EKR Results for Cuspidal Representations of GL2(q)
- Tate cohomology of unipotent cuspidal representations of finite groups of Lie type
- Non-admissible smooth irreducible representations of GL2(F) for totally ramified extensions F/ℚp
BibTeX
@misc{finkelberg2026analogue,
title = {{An analogue of $Γ$-function for irreducible cuspidal representations of the group $\mathrmGL(2)$ over a two-dimensional local field}},
author = {Michael Finkelberg and David Kazhdan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38371},
eprint = {2610.38371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38371},
}
RIS
TY - UNPB
TI - An analogue of Γ-function for irreducible cuspidal representations of the group GL(2) over a two-dimensional local field
AU - Michael Finkelberg
AU - David Kazhdan
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38371
UR - https://arxiv.org/abs/2610.38371
AB - Let F be a non-archimedian local field of odd residue characteristic, 𝒪=F[ [t] ]⊂𝒦=F( (t) ). We consider the subgroup GL̂(2,𝒪)=𝒦^×·GL(2,𝒪)⊂GL(2,𝒦), and the normalizer GL'(2,𝒪)⊂GL(2,𝒦) of an Iwahori subgroup I⊂GL(2,𝒦). We calculate the Γ-functions for irreducible special representations of GL̂(2,𝒪) and GL'(2,𝒪).
ER -