  The algebraicity of critical values of triple product $L$-functions in the
balanced case was proved by Garrett and Harris, under the assumption that the
critical points are on the right and away from center of the critical strip.
The missing right-half critical points correspond to certain holomorphic
Eisenstein series outside the range of absolute convergence. The remaining
difficulties are construction of these holomorphic Eisenstein series and
verification of the non-vanishing of the corresponding non-archimedean local
zeta integrals. In this paper, we address these problems and complement the
result of Garrett and Harris to all critical points. As a consequence, we
obtain new cases of Deligne's conjecture for symmetric cube $L$-functions of
Hilbert modular forms.
