On Borel fixed ideals generated in one degree

We construct a shellable polytopal cell complex that supports a minimal free resolution of a Borel fixed ideal, which is Borel generated by just one monomial in S=k[x1,x2,…,xn]; this includes the case of powers of the homogeneous maximal ideal (x1,x2,…,xn) as a special case. In our most general result we prove that for any Borel fixed ideal I generated in one degree, there exists a polytopal cell complex that supports a minimal free resolution of I.