  We consider a diffusion in $\mathbb{R}^n$ whose coordinates each behave as
one-dimensional Brownian motions, that behave independently when apart, but
have a sticky interaction when they meet. The diffusion in $\mathbb{R}^n$ can
be viewed as the $n$-point motion of a stochastic flow of kernels. We derive
the Kolmogorov backwards equation and show that for a specific choice of
interaction it can be solved exactly with the Bethe ansatz. We then use our
formulae to study the behaviour of the flow of kernels for the exactly solvable
choice of interaction.
