  We consider the gap probability for the Generalized Bessel process in the
single-time and multi-time case. We prove that the scalar and matrix Fredholm
determinants of such process can be expressed in terms of determinants of
Its-Izergin-Korepin-Slavnov integrable kernels and thus related to suitable
Riemann-Hilbert problems. In the single-time case, we construct a Lax pair
formalism, while in the multi-time case we explicitly define a new multi-time
kernel to study.
