  We investigate the intertwining of Laguerre processes of parameter $\alpha$
in different dimensions.
  We introduce a Feller kernel that depends on $\alpha $ and intertwines the
$\alpha$-Laguerre process in $N+1$ dimensions and that in $N$ dimensions.
  When $\alpha $ is a non-negative integer, the new kernel is interpreted in
terms of the conditional distribution of the squared singular values: if the
singular values of a unitarily invariant random matrix of order $(N+\alpha +1)
\times (N+1)$ are fixed, then the those of its $(N+\alpha) \times N $
truncation matrix are given by the new kernel.
