  Generalized multifractality characterizes system size dependence of pure
scaling local observables at Anderson transitions in all ten symmetry classes
of disordered systems. Recently, the concept of generalized multifractality has
been extended to boundaries of critical disordered noninteracting systems. Here
we study the generalized boundary multifractality in the presence of
electron-electron interaction, focusing on the spin quantum Hall symmetry class
(class C). Employing the two-loop renormalization group analysis within
Finkel'stein nonlinear sigma model we compute the anomalous dimensions of the
pure scaling operators located at the boundary of the system. We find that
generalized boundary multifractal exponents are twice larger than their bulk
counterparts. Exact symmetry relations between generalized boundary
multifractal exponents in the case of noninteracting systems are explicitly
broken by the interaction.
