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PreprintarXiv licencearXiv

Homological branching laws for p-adic and mod p representations of GL2 over a p-adic field

  • Yang Chen
  • Haoran Wang
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Abstract

Let F be a finite extension of ℚp and p≥ 5. In this paper, we establish homological branching laws for mod p representations of GL2(F) restricted to split and nonsplit maximal tori, treating principal and special series and, when F=ℚp, supersingular representations. We determine the derived Hom-complexes in both orders for nonexceptional characters. At exceptional characters, we calculate their Euler--Poincaré characteristics under a p-torsion-freeness hypothesis. We also establish corresponding results for a class of unitary Banach space representations.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026homological,
  title = {{Homological branching laws for $p$-adic and mod $p$ representations of $\rm GL_2$ over a $p$-adic field}},
  author = {Yang Chen and Haoran Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29629},
  eprint = {2610.29629},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29629},
}
RIS
TY  - UNPB
TI  - Homological branching laws for p-adic and mod p representations of GL_2 over a p-adic field
AU  - Yang Chen
AU  - Haoran Wang
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29629
UR  - https://arxiv.org/abs/2610.29629
AB  - Let F be a finite extension of ℚ_p and p≥ 5. In this paper, we establish homological branching laws for mod p representations of GL_2(F) restricted to split and nonsplit maximal tori, treating principal and special series and, when F=ℚ_p, supersingular representations. We determine the derived Hom-complexes in both orders for nonexceptional characters. At exceptional characters, we calculate their Euler--Poincaré characteristics under a p-torsion-freeness hypothesis. We also establish corresponding results for a class of unitary Banach space representations.
ER  -