  The three electromagnetic form factors for the transition from a 3/2+ Sigma*
hyperon to the ground-state Lambda hyperon are studied. At low energies,
combinations of the transition form factors can be deduced from Dalitz decays
of the Sigma* hyperon to Lambda plus an electron-positron pair. It is pointed
out how more information can be obtained with the help of the self-analyzing
weak decay of the Lambda. In particular it is shown that these transition form
factors are complex quantities already in this kinematical region. Such
measurements are feasible at hyperon factories as for instance the Facility for
Antiproton and Ion Research (FAIR). At higher energies, the transition form
factors can be measured in electron-positron collisions. The pertinent
relations between the transition form factors and the decay distributions and
differential cross sections are presented. Using dispersion theory, the
low-energy electromagnetic form factors for the Sigma*-to-Lambda transition are
related to the pion vector form factor. The additionally required input, i.e.
the two-pion - Sigma* - Lambda amplitudes are determined from relativistic
next-to-leading-order (NLO) baryon chiral perturbation theory including the
baryons from the octet and the decuplet. A poorly known NLO parameter is fixed
to the experimental value of the Sigma* to Lambda-gamma decay width. Pion
rescattering is taken into account by dispersion theory solving a
Muskhelishvili-Omnes equation. Subtracted and unsubtracted dispersion relations
are discussed. However, in view of the fact that the transition form factors
are complex quantities, the current data situation does not allow for a full
determination of the subtraction constants. To reduce the number of free
parameters, unsubtracted dispersion relations are used to make predictions for
the transition form factors in the low-energy space- and timelike regions.
