sorry for not knowing Maya taht much, but the IMHO more important questionis:
"Which formats is Maya able to read in?"
Normally they should be able to read those standard neutral formats like Parasolid, Step, or some othes.
Now.They use Illustrator import Iges files form 3D CAD and save to AI file to use in Maya software.
As mentioned by @hawcad, you need to check the list of formats that Maya can import against those Solid Edge can export to get the best combination working for you. Sometime there could be issues with the way one pair of formats will import Solid Edge data into Maya.
Also attached is an Excel file with a handy list of import/export options for various software for easy reference. Hope you find it useful.
[ Everything under the sun about - Solid Edge ]
I had pretty good results using JT format to export from Solid Edge to 3dsMax without 3rd party software - perhaps that's something you could try for Maya.