Skip to Main Content

Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Hecke modules and supersingular representations of U(2,1)
HTML articles powered by AMS MathViewer

by Karol Kozioł and Peng Xu PDF
Represent. Theory 19 (2015), 56-93 Request permission

Abstract:

Let $F$ be a nonarchimedean local field of odd residual characteristic $p$. We classify finite-dimensional simple right modules for the pro-$p$-Iwahori-Hecke algebra $\mathcal {H}_C(G,I(1))$, where $G$ is the unramified unitary group $\textrm {U}(2,1)(E/F)$ in three variables. Using this description when $C = \overline {\mathbb {F}}_p$, we define supersingular Hecke modules and show that the functor of $I(1)$-invariants induces a bijection between irreducible nonsupersingular mod-$p$ representations of $G$ and nonsupersingular simple right $\mathcal {H}_C(G,I(1))$-modules. We then use an argument of Paškūnas to construct supersingular representations of $G$.
References
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E50, 20C08, 11F70, 20C20
  • Retrieve articles in all journals with MSC (2010): 22E50, 20C08, 11F70, 20C20
Additional Information
  • Karol Kozioł
  • Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
  • MR Author ID: 1099660
  • Email: karol@math.toronto.edu
  • Peng Xu
  • Affiliation: Mathematics Institute, University of Warwick, Zeeman Building, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 1099916
  • Email: Peng.Xu@warwick.ac.uk
  • Received by editor(s): September 29, 2014
  • Received by editor(s) in revised form: November 25, 2014
  • Published electronically: March 16, 2015
  • Additional Notes: The first author was supported by NSF Grant DMS-0739400.
    The second author was supported by EPSRC Grant EP/H00534X/1.
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 56-93
  • MSC (2010): Primary 22E50, 20C08, 11F70, 20C20
  • DOI: https://doi.org/10.1090/S1088-4165-2015-00462-5
  • MathSciNet review: 3321473