  We present deep optical and infrared observations of the short duration GRB
050906. Although no X-ray or optical/IR afterglow was discovered to deep
limits, the error circle of the GRB (as derived from the Swift BAT) is unusual
incontaining the relatively local starburst galaxy IC328. This makes GRB 050906
a candidate burst from a soft-gamma repeater, similar to the giant flare from
SGR 1806-20. The probability of chance alignment of a given BAT position with
such a galaxy is small (<1%), although the size of the error circle (2.6
arcminute radius) is such that a higher-z origin can't be ruled out. Indeed,
the error circle also includes a moderately rich galaxy cluster at z=0.43,
which is a plausible location for the burst given the apparent preference that
short GRBs have for regions of high mass density. No residual optical or
infrared emission has been observed, either in the form of an afterglow or
later time emission from any associated supernova-like event. We discuss the
constraints these limits place on the progenitor of GRB 050906 based on the
expected optical signatures from both SGRs and merging compact object systems.
