Radio galaxy PKS~1138 $ - $ 262 is a massive galaxy at z = 2.16 , located in a dense environment .
We have found an overdensity of Ly \alpha emitting galaxies in this field , consistent with a proto-cluster structure associated with the radio galaxy .
Recently , we have discovered forty candidate H \alpha emitters by their excess near infrared narrow band flux .
Here , we present infrared spectroscopy of nine of the brightest candidate H \alpha emitters .
All these candidates show an emission line at the expected wavelength .
The identification of three of these lines with H \alpha is confirmed by accompanying [ N ii ] emission .
The spectra of the other candidates are consistent with H \alpha emission at z \sim 2.15 , one being a QSO as indicated by the broadness of its emission line .
The velocity dispersion of the emitters ( 360 km s ^ { -1 } ) is significantly smaller than that of the narrow band filter used for their selection ( 1600 km s ^ { -1 } ) .
We therefore conclude that the emitters are associated with the radio galaxy .
The star formation rates ( SFRs ) deduced from the H \alpha flux are in the range 6 – 44 M _ { \odot } yr ^ { -1 } and the SFR density observed is 5–10 \times higher than in the HDF-N at z = 2.23 .
The properties of the narrow emission lines indicate that the emitters are powered by star formation and contain very young ( < 100 Myr ) stellar populations with moderately high metallicities .