A DESCRIPTION OF THE PROBLEM :
With the default StageStyle, a JavaFX application's stage reacts to the Windows Key Shortcuts to have the application take up one half of the screen—those shortcuts being Win + Left Arrow and Win + Right Arrow.

When the application has the UNDECORATED or TRANSPARENT StageStyles, it *doesn't* react to the Left or Right Shortcuts. Interestingly, though, such stages *do* react to the Windows Key + Up shortcut to maximize them.

DESIRED BEHAVIOR:
Windows Key + Left Arrow: Have application take up up the left half of the current screen.
Windows Key + Right Arrow: Have application take up up the right half of the current screen.


The shortcuts, (from Microsoft: https://support.microsoft.com/en-us/help/12445/windows-keyboard-shortcuts)
Windows logo key + Up arrow Maximize the window.
Windows logo key + Down arrow Remove current app from screen or minimize the desktop window.
Windows logo key + Left arrow Maximize the app or desktop window to the left side of the screen.
Windows logo key + Right arrow Maximize the app or desktop window to the right side of the screen.

AN EXAMPLE APPLICATION:
import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Label;
import javafx.scene.layout.BorderPane;
import javafx.stage.Stage;
import javafx.stage.StageStyle;

public class WindowsKeyShortcut extends Application {
    @Override
    public void start(Stage primaryStage) throws Exception {
        BorderPane root = new BorderPane(new Label("Try the Windows Key with each arrow key."));
        Scene theScene = new Scene(root);
        primaryStage.setScene(theScene);


        primaryStage.initStyle(StageStyle.UNDECORATED);
        primaryStage.show();
    }

}