I'm pretty sure it's a limit but I haven't been able to find any page explaining this notation (see below).
It's from a paper on block maxima. 3 out of 5 occurences:
$V=(-1/logF)^\leftarrow$ (p.4)
$x_n=F^\leftarrow(1-p_n)$ (p.7)
$k_0^{(i)}\sim \frac{n}{(1/s)^\leftarrow (n)}(\frac{\sigma_i^2}{B_i^2})^{1/(1-2\rho)}$ (p.10, most important)
2 more on page 10 related to the last one.
Sometimes you see $f^{\leftarrow}$ as an alternate notation for an inverse function $f^{-1}$. This was proposed to reserve the $-1$ exponent for $1/f$ only. But this has not caught on.
So let's see if this works. What is $V=(-1/\log F)^\leftarrow$? $$ V(\theta)=(-1/\log F)^\leftarrow(\theta)\qquad\Longleftrightarrow\qquad \theta = \frac{-1}{\log(F(V(\theta)))} $$ If so, then $$ \log(F(V(\theta))) = \frac{-1}{\theta} \\ F(V(\theta)) = e^{-1/\theta} \\ V(\theta) = F^{\leftarrow}\big(e^{-1/\theta}\big) $$ Now if $1-p_n = e^{-1/\theta}$, so $-1/\theta=\log(1-p_n)$, and $\theta=-1/\log(1-p_n)$, then we have $$ F^{\leftarrow}(1-p_n) = V\left(-1/\log(1-p_n)\right) $$ as they said.