We have detected the v = 1 \rightarrow 0 ~ { } S ( 1 ) ~ { } ( \lambda = 2.1218 \micron ) and v = 2 \rightarrow 1 ~ { } S ( 1 ) ~ { } ( \lambda = 2.2477 \micron ) lines of H _ { 2 } in the Galactic centre , in a 90 \times 27 arcsec region between the northeastern boundary of the non-thermal source , Sgr A East , and the giant molecular cloud ( GMC ) M-0.02-0.07 . The detected H _ { 2 } ~ { } v = 1 \rightarrow 0 ~ { } S ( 1 ) emission has an intensity of 1.6 – 21 \times 10 ^ { -18 } W m ^ { -2 } arcsec ^ { -2 } and is present over most of the region . Along with the high intensity , the broad line widths ( FWHM = 40 – 70 km s ^ { -1 } ) and the H _ { 2 } ~ { } v = 2 \rightarrow 1 ~ { } S ( 1 ) to v = 1 \rightarrow 0 ~ { } S ( 1 ) line ratios ( 0.3 – 0.5 ) can be best explained by a combination of C-type shocks and fluorescence . The detection of shocked H _ { 2 } is clear evidence that Sgr A East is driving material into the surrounding adjacent cool molecular gas . The H _ { 2 } emission lines have two velocity components at \sim +50 km s ^ { -1 } and \sim 0 km s ^ { -1 } , which are also present in the NH _ { 3 } ( 3,3 ) emission mapped by McGary , Coil , & Ho ( 24 ) . This two-velocity structure can be explained if Sgr A East is driving C-type shocks into both the GMC M-0.02-0.07 and the northern ridge of McGary , Coil , & Ho ( 24 ) .