In his recent book From Hahn-Banach to monotonicity (Springer-Verlag, Berlin, 2008), S. Simons has introduced the notion of SSD space to provide an abstract algebraic framework for the study of monotonicity. Graphs of (maximal) monotone operators appear to be (maximally) q q -positive sets in suitably defined SSD spaces. The richer concept of SSDB space involves also a Banach space structure. In this paper we prove that the analog of the Fitzpatrick function of a maximally q q -positive subset M M in a SSD space \left( B,\left\lfloor \cdot,\cdot \right\rfloor \right) ( B , ⌊ ⋅ , ⋅ ⌋ ) is the smallest convex representation of M M . As a consequence of this result it follows that, in the case of a SSDB space, the conjugate with respect to the pairing \left \lfloor \cdot, \cdot \right \rfloor ⌊ ⋅ , ⋅ ⌋ of any convex representation of M M provides a convex representation of M M , too. We also give a new proof of a characterization of maximally q q -positive subsets of SSDB spaces in terms of such special representations