In my dissertation I proved a certain theorem(s) concerning the representation theory of a direct product G x H of algebraic groups over a field, given those of G and H. But I would wager 100:1 that this theorem is well known, and as such I am looking for a primary reference for it. I have combed (my personal) literature for it, e.g. Jantzen, Humphreys, etc., but cannot find it.

The theorem(s) can be found in section 2 of the following pdf file:

http://homepages.utoledo.edu/mcrumle/references%20needed.pdf

Please ignore the other sections of the file as they pertain to questions having little relevance here.

Thanks in advance for any help.