  We prove a limit theorem concerning the sequence of star-generators of
$S_{\infty}$, where the expectation functional is provided by a character of
$S_{\infty}$ with weights $(w_1, \ldots , w_d, 0,0, \ldots )$ in the Thoma
classification. The limit law turns out to be the law of a "traceless CCR-GUE"
matrix, an analogue of the traceless GUE where the off-diagonal entries
$g_{i,j}$ satisfy the commutation relation $g_{i,j}g_{j,i} = g_{j,i}g_{i,j} +
(w_j - w_i)$. The special case $w_1 = \cdots = w_d = 1/d$ yields the law of a
bona fide traceless GUE matrix, and we retrieve a result of K\"ostler and Nica
from 2021, which in turn extended a result of Biane from 1995.
