Do include the code as well that you are trying that would help to understand your problem better. Based on the understanding that i got about your problem, try this
in XAML:
<Window.InputBindings>
<KeyBinding Modifiers="Windows" Key="D" Command="{Binding YourVMCommand}" CommandParameter="{Binding ElementName=AppWindowName}"/>
</Window.InputBindings>
In View Model set
WindowState = WindowState.Minimized;