Answer: A quick review of several reference sources did not bring up any reference to allelopathic qualities in any of the Aesculus including Aesculus pavia or Red Buckeye. (Black walnut, sunflower, wormwood, sagebrush, and tree of heaven are often cited as examples of allelopathic plants.)
Eventually, I did find one academic citation indicating some or possibly all species of buckeye may have a moderate or slightly allelopathic result from different plant parts including roots, stems, and so on.
I do not remember ever seeing such cautions about planting this tree in the landscape, but on the other hand it is not a widely used tree, either. In fact, Michael Dirr's well respected "Manual of Woody Landscape Plants" makes no mention of it in the discussion of this tree and this is the type of detail one would expect that book to include where applicable.
In my experience, plants can often surprise us and do not always follow exactly what we read about them. It is possible, for instance, that there is a slight allelopathy that can be successfully countered by providing overall excellent cultural conditions for the neighboring plants, or that not all plants are sensitive to it.
If it is an issue of great importance for you in the placement of the tree and what can be grown specifically under or near it, perhaps it would be better to plant something else there just to be on the safe side. If it is not so critical, you might be willing to experiment and see what happens.
You have asked a really interesting question and I'm sorry I can't be more definitive.
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