The Intertwining Property for Laguerre Processes with a Fixed Parameter

We investigate the intertwining of Laguerre processes of parameter α in different dimensions. We introduce a Feller kernel that depends on α and intertwines the α-Laguerre process in N + 1 dimensions and that in N dimensions. When α 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+α+1)×(N+1) are fixed, then the those of its (N+α) × N truncation matrix are given by the new kernel.