Spectral Intertwining Operators
Abstract
We study spectral intertwining operators between spectral Eisenstein series EisP∨, EisQ∨ for two parabolic subgroups $P, Q$ of a p-adic reductive group G with the same Levi subgroup M, inspired by the analogy with the classical intertwining operators between parabolic induced representations of p-adic reductive groups. In particular, we construct the normalized (canonical) intertwining operator that satisfies the transitivity and an unnormalized intertwining operator that is adjoint to a rational section of an analog of the Bruhat-Mackey's filtration. Moreover, the normalized and unnormalized intertwining operators differ by a ratio of L-functions, analogously to the Langlands conjecture about classical ones up to units. Finally we prove that the spectral intertwining operators correspond to classical ones up to units under any conjectural categorical local Langlands correspondence.
Related
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BibTeX
@misc{chen2026spectral,
title = {{Spectral Intertwining Operators}},
author = {Qiyuan Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.17560},
eprint = {2606.17560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17560},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Spectral Intertwining Operators
AU - Qiyuan Chen
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2606.17560
UR - https://arxiv.org/abs/2606.17560
AB - We study spectral intertwining operators between spectral Eisenstein series Eis_P^∨, Eis_Q^∨ for two parabolic subgroups $P, Q$ of a p-adic reductive group G with the same Levi subgroup M, inspired by the analogy with the classical intertwining operators between parabolic induced representations of p-adic reductive groups. In particular, we construct the normalized (canonical) intertwining operator that satisfies the transitivity and an unnormalized intertwining operator that is adjoint to a rational section of an analog of the Bruhat-Mackey's filtration. Moreover, the normalized and unnormalized intertwining operators differ by a ratio of L-functions, analogously to the Langlands conjecture about classical ones up to units. Finally we prove that the spectral intertwining operators correspond to classical ones up to units under any conjectural categorical local Langlands correspondence.
ER -