Should one introduce past work in PhD statement of interest?
I don't think Ben's answer says this strongly enough:

Your statement must include a description of your past work, if you have any.

The primary feature that PhD admissions committees looking for in applicants is evidence of potential for high-quality independent research.  The strongest possible evidence of your potential to do high-quality independent research is the fact that you have actually published high-quality independent research. 

It doesn't matter whether your past research is on the same topics that you want to pursue in the future.  It's easy to communicate a change in interests in your statement with a single sentence: "More recently, however, my interests have shifted to quantum tropical M-theory."  (Obviously this sentence should be followed by a description of your specific interests in quantum tropical M-theory, written with enough maturity to convince experts in quantum tropical M-theory that you have the necessary knowledge and skills to be successful in quantum tropical M-theory, but that's what you were going to write anyway.)

Crucially, if your previous papers have coauthors, your statement (and your recommendation letters!) should focus on your specific technical contributions to those papers.  Remember that you are not trying to sell the work as good mathematics; you are trying to sell yourself as a good mathematician.

In particular, you are not trying to sell your past work to experts in your subsubfield of (past) interest, so you should not merely quote the abstracts.  You are trying to sell yourself to a general audience of trained mathematicians, some of whom are experts in your subsubfield of (past) interest.  So your description needs to be understandable to that broader audience, but still interesting enough to experts that they will want to read your papers for the actual technical details.

Obviously you should provide direct links to arXiv versions of your papers, in both your CV and your statement, so that interested committee members can read them without having to search.

[I'm an American theoretical computer scientist, which means I'm like a mathematician, except that I write less code.]