Yes, you landlord is obligated to fix a broken window, by the "implied warranty of habitability"--the obligation  placed on landlords by law that all rental properties be "fit for their intended purpose." A broken window can let rain in, let intruders in, affect temperature, etc., and therefore would violate this warranty (this is assuming a major break; the landlord likely would not have to repair or replace if there's a small crack, but the pane is fundamentally intact).