Is there any difference between 'represent' and 'represent for'?

There is only one interpretation that I can find licensed.

This demands that 'represent' be used as an intransitive verb here; 'When should I use "represent for"?' then becomes a poor question. With this transitive usage, it is clear that the string 'represents for' is accidental (I've added commas to make the grammar clearer):

He represents, for the average woman, the ideal husband.

RHKWebster's has this intransitive usage:

represent v.i. 11. to protest.

So one could possibly write

He represented for democracy

(and certainly They protested / represented for months).