What is the hybridization of the central iodine atom in I3−?

##sp^3d##

The easiest way to determine this is to draw the lewis structure of the species. What's important here is knowing that the species, ##I## can become hypervalent, or that is, it will disobey the by expanding its valency to accept more than eight electron around it.

Another good example of a species which does this is ##XeF_4##.

Consider below:

Remember when forming hybrid orbitals, we always know that we must:

use ##n## atomic orbital to make ##n## hybrid orbitals

and

for ##n=5## we know that we make ##sp^3d## hybrids.