  There has been a very recent surge in the interest on the localization
properties of resonances associated to partially open (scattering) systems,
which are of great relevance when studying resonant cavities such as those used
in microlasers. Very recently, it has been found that no localization is
present in a scaled form of these states. Moreover, a new kind of scarring on
structures different from periodic orbits is described for non scaled
resonances. In this paper, we analyze the localization of a distribution
function corresponding to the quantum LR representation -- based on the non
unitary evolution operator decomposition into left and right resonances -- for
the partially open quantum tribaker map, a paradigmatic system. We find
localization on the shortest periodic orbits. Also, scaled states present
enhancements that could not be associated to periodic orbits and that become
more evident when looking at the LR representation. These findings open the
door for new perspectives on recent theoretical developments.
