I don't know the direct answer to your question, but here's a forum right here at GW I discovered recently that will have your answer!

allelopathy (adj. allelopathic)
The inhibition of growth of one plant species by another due to the release of chemical substances.

Here is a link that might be useful: Allelopathy

Hey Drayven ,
Well....
Apparently I missed that memo, ;-)
I didn't know that you weren't supposed to plant them near each other. I have been growing them right on top of each other (damn near) and they don't give me any grief ,but they do grow,and grow and grow ;-),
I have not noticed any issues.... in the last 3 years.

You could do a little experiment and plant some together and some apart and see if they do differently.

I'll admit, I don't plant them together just to be on the safe side, and because no situation has arisen where I really needed to plant them together. But it's possible that it's bunk. Or it's possible that it's true and just hasn't been tested or we don't know why it works.

I know a guy who swears that castrating his steers on the proper moon phase (according to the Farmer's Almanac) made a HUGE difference compared to when he didn't. So I gotta hand it to the guy that he at least tested it, even though I still don't see how moon phases would make any difference. So far I've been too lazy to test out much of the garden folklore I've read.

Any other plant that can grow into the onion row or lay over onion plants will hinder their growth. If you want a good onion crop plant it with other onions and weed it well. More bulb onion growers including myself are planting onions on plastic mulch. You can usually set 4 onion rows to a 4 foot layed strip of black plastic. Onions do so much better with no competition from other plants.

I know from experience that allium can be allelopathic toward some legumes, specifically, pisum. The effect from perennial walking onion on spring-planted peas has been very pronounced, such that occasionally some pea-plants have been a near-total loss. However, the peas have to be quite near the root-zone of the onions, and if the onions are pulled a few weeks or months before planting peas there doesn't seem to be any problem.

Annually-grown onions are quite unlikely to be a problem, since peas are planted well before started onions are set out and it would be months before the onion roots would be robust enough to exude serious quantities of whatever it is that the peas don't like, and of course by then peas are pretty much gone by. That's why most gardeners never have encountered this mis-companionship. I suspect that in the days when walking onions were quite common the conflict was well known, and the tale still gets told though tradition has changed.

I didn't know either and pretty much planted them on top of each other and they did great

Mine grow great right next to each other (I am in snap pea heaven right now). Garlic too. You can get past the N issue Digdirt correctly raised by drenching the onions narrowly with compost tea & fish emulsion. But I have CA coastal clay so I can always err on the side of extra humic acids safely. Plus, if you inoculate your legumes, you surely must gain more yield than any small alleopathic root war would cost.

All these accounts bear out the fact that this allelopathy of allium upon pisum is rarely a problem for gardeners.

Why then does this story perennially arise? I believe I have explained it. BTW, walking onion is a very useful plant, even if one has to be careful to keep it away from the peas.....

Does this allelopathy include other members of the legume family? I have a white runner bean pretty close to some walking onions. Both the walking onions and the bean are young. What is the safe distance? Is it the root network or more?

I have observed garlic-pole beans poor growth (by both), when planted very close to one another.

IME, beans generally are not as adversely effected.

For peas, when the vigorous roots of walking onion - during the spring when the onion plants are really robustly growing - come within a foot or so of a pea-row, is when I see significant negative effect. The root zone of a walking onion can be a foot to eighteen inches out all around on a big plant.

I went a little overboard planting onion sets one year, and ended up sticking some in very close with my snap peas. Those particular snap peas only grew 1/3 as tall, as the same snap peas that were not snuggling up to onions. Now, as I work in research, I know this is far from enough evidence to come to a conclusion that onions DO indeed harm peas, however, as I have plenty of space to keep the two separate, I do not plant onions interspersed with peas anymore.

Root Development of Vegetable Crops has a chapter on onions and a chapter on peas.

I would suspect that if one were wanting to study peas and onions together the link to root development might be interesting. Hint on using the linked site, skip directly to the area of your interest,