  We present clear spectroscopic detections of molecular hydrogen in the outer
filaments of the H-alpha nebula surrounding the central galaxy of the Perseus
cluster, NGC 1275. This implies the presence of warm molecular gas clouds at
projected distances up to 24 kpc from the nucleus of the host galaxy, embedded
in the hot intracluster medium. The emission-line intensity ratios reveal that
the molecular hydrogen is predominately thermally excited with excitation
temperatures of 1600-2200K, suggesting a lack of pressure balance between the
molecular component and its surrounding medium. Excitation by stellar UV or by
the central AGN is shown to be unlikely, whilst thermal excitation by X-rays or
conduction from the ICM or shocks are all possibilities. Evidence for a
non-thermal component is found in the spectra of some regions based on a low
ortho-to-para ratio.
