Can you hang a copy of a published poem without permission?

Technically this is illegal (a breach of copyright) - but if an author objected he would merely be entitled to ask you to 'cease and desist' (take it down). As long as you take it down when (if) you are asked - no problem.

Most authors would be happy to give you permission to hang their poem, if you asked them. Why not email the author in question and ask?