Hecke modules and supersingular representations of U(2,1)
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- by Karol Kozioł and Peng Xu
- Represent. Theory 19 (2015), 56-93
- DOI: https://doi.org/10.1090/S1088-4165-2015-00462-5
- Published electronically: March 16, 2015
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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
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Bibliographic 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