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I am currently writing a paper where I need talk both about a representation of a semisimple Lie group (usually denoted by $\rho$), and about spectral radii of linear maps (also usually denoted by $\rho$). Those two notations really clash, because if $g$ is an element of the Lie group, $\rho(g)$ can make perfect sense both ways. (The worst is when I wish to talk about the spectral radius of $g$ in a given representation...)

Surely I am not the first mathematician to encounter this problem. Could anyone give a widely-recognized alternative notation either for a representation or for the spectral radius?

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    $\begingroup$ I often use $r(a)$ for the spectral radius of an element of a (Banach) algebra $\endgroup$
    – Yemon Choi
    Apr 18, 2016 at 16:07
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    $\begingroup$ $\pi$ and $\sigma$ are often used for representations. Really, you should feel free to use almost any letter for a representation. $\endgroup$
    – S. Carnahan ♦
    Apr 18, 2016 at 16:15
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    $\begingroup$ Well if you're not very pedantic, you can omit the representation notation and just write $g.v$. $\endgroup$
    – Asaf
    Apr 18, 2016 at 16:27
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    $\begingroup$ Also in Lie theory isn't $\rho$ most commonly used for the half-sum of positive roots? $\endgroup$
    – Sam Hopkins
    Apr 18, 2016 at 17:03
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    $\begingroup$ Okay, suggestion #2- this notation have been used (although not the most common) in dynamics - for $g.v$ just write $T_{g}(v)$, and if you have several representations,just write $S_{g}(v)$ or index them somehow. BTW if you are not using anything about ranks, I think that it would be more than reasonable to write $r(A)$ for the radius of operator $A$ (this notation is sometime used for rank of operator,which coincidentally sometime denoted by $\rho$ as well), so the bottom line is that you should choose a reasonable notation, declare it clearly in the beginning of your paper, and stick to it. $\endgroup$
    – Asaf
    Apr 19, 2016 at 8:43

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