Keating and Snaith have a famous conjecture on the asymptotics of the integral $\int_0^T |\zeta(\frac 12+it)|^{2k}\, dt$, where $\zeta$ denotes the Riemann zeta function. See page 510 of the book review by Brian Conrey of H. Iwaniec, Lectures on the Riemann zeta function in Bull. Amer. Math. Soc. 53 (2016), 507--512 (http://www.ams.org/journals/bull/2016-53-03/S0273-0979-2016-01525-4/S0273-0979-2016-01525-4.pdf). This conjecture involves a certain number $g_k$. This number is equal to the number of standard Young tableaux whose shape is a $k\times k$ rectangle. Equivalently, this is the degree of the irreducible representation of the symmetric group $S_{k^2}$ corresponding to this shape. Is there any (conjectural) explanation for this connection between $\zeta(s)$ and the representation theory of $S_{k^2}$? Does the degree of other irreps of $S_n$ (for suitable $n$) also have connections with the asymptotics of $\zeta(s)$?