Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles
Abstract
In this paper we give a geometric description of the behavior of analytic intertwining operators between parabolically induced representations of GLn(F), where F is a local non-archimedean field, in terms of hyperbolic localization functors of Braden. As a consequence, we can show that the image of an intertwining operator is always semi-simple and give a lower bound on the order of its pole, which is conjectured to be an equality as well as an upper bound in terms of the singular support of certain perverse sheaves. Moreover, we are able to reduce the conjecture of Lapid and Mínguez on the shape of irreducible subrepresentations of induced representations to a computation of characteristic cycles. The theory of mixed Hodge modules plays a crucial role in the proofs.
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BibTeX
@misc{droschl2026generalized,
title = {{Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles}},
author = {Johannes Droschl},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.29312},
eprint = {2608.29312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29312},
}
RIS
TY - UNPB
TI - Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles
AU - Johannes Droschl
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2608.29312
UR - https://arxiv.org/abs/2608.29312
AB - In this paper we give a geometric description of the behavior of analytic intertwining operators between parabolically induced representations of GL_n(F), where F is a local non-archimedean field, in terms of hyperbolic localization functors of Braden. As a consequence, we can show that the image of an intertwining operator is always semi-simple and give a lower bound on the order of its pole, which is conjectured to be an equality as well as an upper bound in terms of the singular support of certain perverse sheaves. Moreover, we are able to reduce the conjecture of Lapid and Mínguez on the shape of irreducible subrepresentations of induced representations to a computation of characteristic cycles. The theory of mixed Hodge modules plays a crucial role in the proofs.
ER -