On the existence of admissible supersingular representations of $p$-adic reductive groups

Florian Herzig; Karol Koziol; Marie-France Vignéras

doi:10.1017/fms.2019.50

On the existence of admissible supersingular representations of $p$-adic reductive groups

Representation Theory 2020-05-05 v3

Authors: Florian Herzig , Karol Koziol , Marie-France Vignéras

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Suppose that $\mathbf{G}$ is a connected reductive group over a finite extension $F/\mathbb{Q}_p$ , and that $C$ is a field of characteristic $p$ . We prove that the group $\mathbf{G}(F)$ admits an irreducible admissible supercuspidal, or equivalently supersingular, representation over $C$ .

Keywords

p-adic reductive groups admissible representations supersingular representations supercuspidal representations connected reductive group

Cite

@article{arxiv.1905.00053,
  title  = {On the existence of admissible supersingular representations of $p$-adic reductive groups},
  author = {Florian Herzig and Karol Koziol and Marie-France Vignéras},
  journal= {arXiv preprint arXiv:1905.00053},
  year   = {2020}
}

Comments

58 pages, with an appendix by Sug Woo Shin. This replaces arXiv:1712.10142 and arXiv:1808.08255. v2: Minor changes following referee report; to appear in Forum Math. Sigma

On the existence of admissible supersingular representations of $p$-adic reductive groups

Abstract

Keywords

Cite

Comments

Related papers