Generic Trivial Source Character Tables of \(\mathrm{PSL}_2(q)\) and \(\mathrm{SL}_2(q)\)

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• [BFL22] B. Böhmler, N. Farrell and C. Lassueur, Trivial source character tables of \(\mathrm{SL}_2(q)\), Part I,
  J. Algebra 598 (2022), 308-350. [doi | arXiv | Oberwolfach Preprint]
  contains the following cases:
  • q odd, \(\ell\) odd, \(\ell\mid (q\pm 1)\)
  • q odd, \(\ell=2\), \( q\equiv\pm 3\pmod{8}\)
• [FL23] N. Farrell and C. Lassueur, Trivial source character tables of \(\mathrm{SL}_2(q)\), Part II,
  Proc. Edinburgh Math. Soc. 66 (2023), 689-709. [doi | arXiv]
  contains the following cases:
  • q even, \(\ell\mid (q\pm 1)\)
• Open: defining characteristic

Here \(\ell\) denotes the characteristic of the field over which we do representation theory, not the defining characteristic of the groups.