Research into plant interaction is quite limited and few are specific. There have been generalizations based on observation. The past 20 years has seen increased interest in the mechanisms and consequences.

I have linked a Plant Physiology article that updates recent studies. Further searching may locate some of the specific companion relationships of vegetables. Of interest are the sections on root-rhizosphere communication, alteration of soil characteristics, and cellular mechanisms of root exudation.

To date I recognize that soil organism dominence (i.e. - bacterial versus fungal) may be a factor. Also of merit are the potentials of defensive and allelopathic effects.

Any article finding of related interest can be posted in this thread. On with the learning.

Here is a link that might be useful: Root Exudation and Rhizosphere Biology