Quote Originally Posted by TATY
любимый, любимая, любимое, любимые = (being) loved (long form) [also 'favourite']
любим, любима, любимо, любимы = short form
Here любим is the short form present passive participle NOT the the present tense verb form "мы любим".

Любим кем? = Loved by whom (instrumental)
Любим библиотекарями = Loved by librarians.
Right! To avoid a confusion, I think we just have to clarify that the stress is different as well:
present tense Мы любим.
participle form любим, (любима, любимо, любимы).