I've read that both ar an Luan and Dé Luain mean "on mondays". Does one refer to mondays in general and the other one to a specific monday?
Dé Luain is generally “on (a specific) Monday”, but could mean “on Mondays” in a sentence with a verb that has a habitual aspect.
In Hiberno-English we say "On THE Monday" usually to mean a Monday in the future, not necessarily next Monday. "Ar an Luan" has nothing to indicate plurality so I think it's wrong to say it means "on Mondays."
You can't apply the rules of one language to another language. This may not make sense in English, but this is Irish -- ar an Luan = on Mondays.
Would it be wrong to put the noun into the plural form when it means generally - "on Mondays"?