A note on presentations of supersingular representations of $\text{GL}_2(F)$

Zhixiang Wu

doi:10.1007/s00229-020-01224-z

A note on presentations of supersingular representations of $\text{GL}_2(F)$

Representation Theory 2021-03-09 v2 Number Theory

Authors: Zhixiang Wu

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Abstract

We prove that any smooth irreducible supersingular representation with central character of $\text{GL}_2(F)$ is never of finite presentation when $F$ is a finite field extension of $\mathbb{Q}_p$ such that $F\neq \mathbb{Q}_p$ , extending a result of Schraen for quadratic extensions.

Keywords

supersingular representations finite presentation GL_2(F) smooth irreducible representations central character local fields

Cite

@article{arxiv.1911.12030,
  title  = {A note on presentations of supersingular representations of $\text{GL}_2(F)$},
  author = {Zhixiang Wu},
  journal= {arXiv preprint arXiv:1911.12030},
  year   = {2021}
}

Comments

12 pages, final version

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