The Galactic center influences the current nature as well as the formation, evolution, and the fate of the Milky Way. The Galactic nucleus is representative of the galactic nuclei of other galaxies and provides an opportunity to study the environment around a supermassive black hole (SMBH) at high spatial resolution. The central 10 pc of the Galaxy, the Sgr A region, contains several principal components: the SMBH candidate (Sgr A*), the central cluster, the circumnuclear disk (CND), Sgr A West, a powerful supernova-like remnant (Sgr A East), and surrounding molecular clouds. Developing a consistent picture of the interactions between these components will improve our understanding of the Galaxy and the nature of galactic nuclei in general. Previous studies of the spatial and dynamical relationships between the various objects have been mostly based on indirect and qualitative evidence and leave unsolved many questions that require more robust evidence. Molecular hydrogen (H2) emission has been used as an excellent tracer and diagnostic for interactions between dense molecular clouds and hot, powerful sources. We observed the H2 (1 0) S(1) (l p 2.1218 mm) and H2 (2 1) S(1) (l p 2.2477 mm) emission-line spectra from the interaction regions between Sgr A East, the CND, and the surrounding molecular clouds. Using the long-slit Cooled Grating Spectrometer 4 (CGS4) with an echelle grating at the 3.8 m United Kingdom Infrared Telescope (UKIRT) on Mauna Kea, Hawaii, we scanned 56 positions in the interaction regions. We reduced two-dimensional spectral images using IRAF and analyzed a three-dimensional data cube using MIRIAD. The data cube has the H2 information both in space (with a resolution of ∼2 ) and in velocity (with a resolution of ∼18 km s ). The H2 (1 0) S(1) data cube was directly compared with the NH3 (3, 3) data cube from McGary et al. (2001, ApJ, 559, 326) to investigate gas kinematics. Based on the H2 (1 0) S(1) and (2 1) S(1) line intensities and gas kinematics, we concluded that the H2 excitation can be explained by two mechanisms: a combination of fluorescence and C-shocks in very strong magnetic fields, or a mixture of slow C-shocks and fast J-shocks. We estimated shock velocities (∼100 km s ) of Sgr A East by comparing H2 line profiles with those of NH3. From the distribution of the shocked H2 emission, we determined the interacting boundary of Sgr A East in projection to be an ellipse, with the center at ∼1.5 pc offset from Sgr A*, and a dimension of 10.8 # 7.6 pc. We also determined the positional relationship between Sgr A East and the molecular clouds along the line of sight and suggested a revised model for the three-dimensional structure of the central 10 pc. From the estimated shock velocities, we deduced the initial explosion energy ([0.2–4] # 10 ergs) of Sgr A East. This extremely large energy excludes the hypothesis of a single, typical supernova (SN) for the origin of Sgr A East. We examined other hypotheses (tidal disruption of a star by the SMBH, multiple supernovae, and a hypernova) and we concluded that a hypernova (collapsar or microquasar) is the most probable origin of Sgr A East. Based on the energy, we investigated the influence of Sgr A East–like explosions (hypernovae) and normal SNe on the mass inflow to the Galactic nucleus. We suggest a scenario in which the continuous mass inflow into the Galactic nucleus makes it active by igniting the SMBH or stimulating a starburst every ∼108 yr, but each active phase continues for only 10 yr, since a large number of SNe resulting from newly born massive stars quickly stop the mass supply. The Galactic nucleus is likely to spend only about 1/10 of its life as active. As for the recent history of the central 10 pc, the mass inflow restarted several 10 yr ago after a quiescent phase, for ∼108 yr. In its usual schedule, the Galactic nucleus would continue its activity for a few 10 yr more before a huge number of SNe would occur. However, the active phase was unexpectedly stopped ∼104 yr ago by Sgr A East.