A SU(2) recipe for mutually unbiased bases

v2: abstract enlarged, a corollary added, acknowledgments added, one reference added, presentation improved; v3: two misprints correctedA simple recipe for generating a complete set of mutually unbiased bases in dimension (2j+1)**e, with 2j + 1 prime and e positive integer, is developed from a single matrix acting on a space of constant angular momentum j and defined in terms of the irreducible characters of the cyclic group C(2j+1). As two pending results, this matrix is used in the derivation of a polar decomposition of SU(2) and of a FFZ algebra