Associated graded modules for modular representations of quaternion algebras

Jiusi Zhao

Associated graded modules for modular representations of quaternion algebras

Representation Theory 2026-07-30 v1

Authors: Jiusi Zhao

Abstract

Let $K$ be a finite unramified extension of $\mathbb{Q}_p$ and $D$ the non-split quaternion algebra over $K$ . We compute the associated graded modules of the duals of the predicted representations of $D^\times$ occurring in the Jacquet--Langlands correspondence.

Keywords

quaternion algebras modular representations associated graded modules Jacquet-Langlands correspondence p-adic representations

Cite

@article{arxiv.2607.28748,
  title  = {Associated graded modules for modular representations of quaternion algebras},
  author = {Jiusi Zhao},
  journal= {arXiv preprint arXiv:2607.28748},
  year   = {2026}
}