On the characters of Sylow $p$-subgroups of finite Chevalley groups $G(p^f)$ for arbitrary primes
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Abstract:
In this work we develop a method to parametrize the set $\mathrm {Irr}(U)$ of irreducible characters of a Sylow $p$-subgroup $U$ of a finite Chevalley group $G(p^f)$ which is valid for arbitrary primes $p$, in particular, when $p$ is a very bad prime for $G$. As an application, we parametrize $\mathrm {Irr}(U)$ when $G=\mathrm {F}_4(2^f)$.References
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Additional Information
- Tung Le
- Affiliation: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
- Email: lttung96@yahoo.com
- Kay Magaard
- Affiliation: Department of Mathematics, University of Arizona, 617 Santa Rita Road, Tuscon, Arizona 85721
- MR Author ID: 252279
- Alessandro Paolini
- Affiliation: FB Mathematik, Technische UniversitΓ€t Kaiserslautern, 67653 Kaiserslautern, Germany
- MR Author ID: 1178905
- Email: paolini@mathematik.uni-kl.de
- Received by editor(s): January 31, 2019
- Received by editor(s) in revised form: July 29, 2019
- Published electronically: November 19, 2019
- Additional Notes: Part of this work has been developed during visits: of the second author at the University of Pretoria and at the University of KwaZulu-Natal in June 2018, supported by CoE-Mass FA2018/RT18ALG/007; of the second author in June 2018 and of the first author in January 2019 at the Technische UniversitΓ€t Kaiserslautern, supported by the SFB-TRR 195 βSymbolic Tools in Mathematics and their Applicationβ of the German Research Foundation (DFG) and NRF Incentive Grant 109304; and of the third author in September and October 2018 at the Hausdorff Institute of Mathematics in Bonn during the semester βLogic and Algorithms in Group Theoryβ, supported by a HIM Research Fellowship
The third author acknowledges financial support from the SFB-TRR 195 - © Copyright 2019 American Mathematical Society
- Journal: Math. Comp. 89 (2020), 1501-1524
- MSC (2010): Primary 20C33, 20C15; Secondary 20C40, 20G41
- DOI: https://doi.org/10.1090/mcom/3488
- MathSciNet review: 4063326