Shulchan Aruch, Orach Chayim 112:2:
"One should not recite liturgical poems during [the shemoneh esreh] prayer."
Mishnah Berurah, ad loc:
"In the responsum of Radvaz, v. III, responsum 532, [Radvaz] wrote at length to permit this (and he wrote that he has in his hand some inquiries that one of the rishonim asked of heaven via meditative seclusion (hithbodeduth) and prayer and invocation of names, and they responded to his inquiries, and he asked also about this [matter of liturgical poems] and they answered him that it is permitted). See there that [Radvaz] cautions strongly not to alter the [accepted] custom [to recite them]."
