Del Junco–Lemańczyk [Generic spectral properties of measure-preserving maps and applications. Proc. Amer. Math. Soc., 115 (3) (1992)] showed that a generic measure-preserving transformation satisfies certain orthogonality conditions. More precisely, there is a dense 
$G_{\unicode[STIX]{x1D6FF}}$ subset of measure preserving transformations such that, for every 
$T\in G$ and 
$k(1),k(2),\ldots ,k(l)\in \mathbb{Z}^{+}$, 
$k^{\prime }(1),k^{\prime }(2),\ldots ,k^{\prime }(l^{\prime })\in \mathbb{Z}^{+}$, the convolutions 
$$\begin{eqnarray}\unicode[STIX]{x1D70E}_{T^{k(1)}}\ast \cdots \ast \unicode[STIX]{x1D70E}_{T^{k(l)}}\quad \text{and}\quad \unicode[STIX]{x1D70E}_{T^{k^{\prime }(1)}}\ast \cdots \ast \unicode[STIX]{x1D70E}_{T^{k^{\prime }(l^{\prime })}},\end{eqnarray}$$
$\unicode[STIX]{x1D70E}_{T^{k}}$ is the maximal spectral type of 
$T^{k}$, are mutually singular, provided that 
$(k(1),k(2),\ldots ,k(l))$ is not a rearrangement of 
$(k^{\prime }(1),k^{\prime }(2),\ldots ,k^{\prime }(l^{\prime }))$. We will introduce analogous orthogonality conditions for continuous unitary representations of the group of all measurable functions with values in the circle, 
$L^{0}(\unicode[STIX]{x1D707},\mathbb{T})$, which we denote by the DL-condition. We connect the DL-condition with a result of Solecki [Unitary representations of the groups of measurable and continuous functions with values in the circle. J. Funct. Anal., 267 (2014), pp. 3105–3124] which identifies continuous unitary representations of 
$L^{0}(\unicode[STIX]{x1D707},\mathbb{T})$ with a collection of measures 
$\{\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D705}}\}$, where 
$\unicode[STIX]{x1D705}$ runs over all increasing finite sequence of non-zero integers. In particular, we show that the ‘probabilistic’ DL-condition translates to ‘deterministic’ orthogonality conditions on the measures 
$\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D705}}$. As a corollary, we show that the same orthogonality conditions as in the result by Del Junco–Lemańczyk hold for a generic unitary operator on a separable infinite-dimensional Hilbert space.
