The matrix multiplication is Dot
in Mathematica. If you need your product for display only, you can inactivate it:
Inactive[Dot][g[t - 1], g[t - 2], \[Ellipsis], g[2], g[1]]
If you need it for actual calculation you can use the infix form of Dot
:
g[5].g[4].g[3].g[2].g[1]
or generate the terms with Table
:
Dot @@ Table[g[k], {k, 5, 1, -1}]