Molecular species, most frequently H_2, are present in a small, but growing, number of gamma-ray burst (GRB) afterglow spectra at redshifts z~2-3, detected through their rest-frame UV absorption lines. In rare cases, lines of vibrationally excited states of H_2 can be detected in the same spectra. The connection between afterglow line-of-sight absorption properties of molecular (and atomic) gas, and the observed behaviour in emission of similar sources at low redshift, is an important test of the suitability of GRB afterglows as general probes of conditions in star formation regions at high redshift. Recently, emission lines of carbon monoxide have been detected in a small sample of GRB host galaxies, at sub-mm wavelengths, but no searches for H_2 in emission have been reported yet. In this paper we perform an exploratory search for rest-frame K band rotation-vibrational transitions of H_2 in emission, observable only in the lowest redshift GRB hosts (z<0.22). Searching the data of four host galaxies, we detect a single significant rotation-vibrational H_2 line candidate, in the host of GRB 031203. Re-analysis of Spitzer mid-infrared spectra of the same GRB host gives a single low significance rotational line candidate. The (limits on) line flux ratios are consistent with those of blue compact dwarf galaxies in the literature. New instrumentation, in particular on the JWST and the ELT, can facilitate a major increase in our understanding of the H_2 properties of nearby GRB hosts, and the relation to H_2 absorption in GRBs at higher redshift.
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