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The minimal projective degrees (minimal degree of an irreducible representation of a central extension) of the finite classical groups are (famously) given by Tiep and Zalesskii [1]. Is there a convenient reference for the minimal ordinary degrees?

[1] Pham Huu Tiep; Zalesskii, Alexander E., Minimal characters of the finite classical groups, Commun. Algebra 24, No. 6, 2093-2167 (1996). ZBL0901.20031.

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  • $\begingroup$ "Minimal ordinary degree" = minimal degree of a nontrivial irrep.? This seems related: mathoverflow.net/questions/400864/… $\endgroup$
    – Sam Hopkins
    Commented Dec 11, 2021 at 14:22
  • $\begingroup$ Right: ordinary as opposed to projective. That question is related, but note that projective degrees are often smaller. E.g., the minimal degree of $A_5$ is $3$, but since the universal cover of $\mathrm{SO}(3)$ is $\mathrm{SU}(2)$ it has a 2-fold cover (the binary icoasahedral group) with a 2-dimensional complex representation. $\endgroup$
    – Sean Eberhard
    Commented Dec 11, 2021 at 14:26
  • $\begingroup$ Sorry, I'm confused. The linked question is about ordinary representations, which is what you're also asking about, right? Also: is it important that the representation be faithful? $\endgroup$
    – Sam Hopkins
    Commented Dec 11, 2021 at 17:51
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    $\begingroup$ Uh, yes. OK what I should have said is I'm looking for a more precise answer. E.g., what is the exact minimal degree of $\mathrm{PSp}_{2n}(q)$ etc for all $n$ and $q$. $\endgroup$
    – Sean Eberhard
    Commented Dec 11, 2021 at 19:59
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    $\begingroup$ Because I'm asking about simple groups, nontrivial representations are automatically faithful. $\endgroup$
    – Sean Eberhard
    Commented Dec 11, 2021 at 20:00

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