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Generic distinction of induced representations: the case of symmetric spaces
Abstract
Let H be the fixed-point subgroup of an involution of a reductive group G over a local field F of characteristic zero. We give a necessary condition for a parabolically induced representation of G(F) to admit a non-zero family of H(F)-equivariant linear forms depending holomorphically on the induction parameter. By works of Blanc-Delorme and Brylinski-Delorme, this condition is essentially sufficient. As a global consequence, we obtain vanishing results for regularized periods of Eisenstein series. We illustrate this on symplectic periods, where we extend Offen's computation of truncated periods of certain cuspidal Eisenstein series to inner forms of GL(2n).
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BibTeX
@misc{chaudouard2026generic,
title = {{Generic distinction of induced representations: the case of symmetric spaces}},
author = {Pierre-Henri Chaudouard and Cheng Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27458},
eprint = {2610.27458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27458},
}
RIS
TY - UNPB
TI - Generic distinction of induced representations: the case of symmetric spaces
AU - Pierre-Henri Chaudouard
AU - Cheng Chen
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27458
UR - https://arxiv.org/abs/2610.27458
AB - Let H be the fixed-point subgroup of an involution of a reductive group G over a local field F of characteristic zero. We give a necessary condition for a parabolically induced representation of G(F) to admit a non-zero family of H(F)-equivariant linear forms depending holomorphically on the induction parameter. By works of Blanc-Delorme and Brylinski-Delorme, this condition is essentially sufficient. As a global consequence, we obtain vanishing results for regularized periods of Eisenstein series. We illustrate this on symplectic periods, where we extend Offen's computation of truncated periods of certain cuspidal Eisenstein series to inner forms of GL(2n).
ER -