Year: 2026
Type: preprint
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).
Source: arXiv (Cornell University)
Authors: Chaudouard, Pierre-Henri, Chen, Cheng
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223114215