First, by alkalinity do you mean carbonate hardness? Or are you using the term in the former sense of a pH above 7 which is today more often termed "basic?"
Alkalinity as carbonate hardness is connected to the GH because both have to do with minerals like calcium primarily and magnesium. Alkalinity buffers the pH, preventing fluctuations, so the higher the Alkalinity the more the pH will resist efforts to change it.
The only safe and effective way to lower the Alkalinity is by diluting the water with some form of "pure" water, such as distilled, reverse osmosis or sometimes rainwater. This will simultaneously reduce the GH and KH (Alkalinity) in proportion. At the same time, the pH usually lowers as well, since the three are connected.
Is this "high Alkalinity" in your source water itself (tap water)? Or just in the water after it has been in the aquarium? The latter would indicate that something calcareous in thee aquarium (rock or substrate composed of a calcareous mineral such as calcium, aragonite, dolomite, limestone, marble, coral) is affecting the GH/KH/pH. And can you give us the number and unit of measurement for the GH, KH (Alkalinity) and pH?
Byron.