  We discuss kernels on complact classical groups $G=\U(n)$, $\OO(2n)$,
$\Sp(n)$ defined by the formula $K(z,u)=|\det(1-zu^*)|^s$. We obtain the
explicit Plancherel formula for these kernels and the interval of
positive-definiteness. We also obtain explicit models for Sahi's 'unipotent'
representations.
