  Phenomenological representations of generalized parton distributions (GPDs)
implementing the non-trivial field theoretical requirements are employed in the
present day strategies for extracting of hadron structure information encoded
in GPDs from the observables of hard exclusive reactions. Showing out the
equivalence of various GPD representations can help to get more insight into
GPD properties and allow to build up flexible GPD models capable of
satisfactory description of the whole set of available experimental data. We
review the mathematical aspects of establishing equivalence between the the
double partial wave expansion of GPDs in the conformal partial waves and in the
$t$-channel ${\rm SO}(3)$ partial waves and the double distribution
representation of GPDs.
