GridSplitter simple scenario

Hi,

I defined 3 columns, two of them being tied up. I defined also a GridSplitter. But in the following scenario user is not able to move splitter to any direction. Why it is not possible?

<Grid IsSharedSizeScope="True">
<Grid.ColumnDefinitions>
<ColumnDefinition SharedSizeGroup="a"></ColumnDefinition>
<ColumnDefinition></ColumnDefinition>
<ColumnDefinition SharedSizeGroup="a"></ColumnDefinition>
</Grid.ColumnDefinitions>

<TextBox Height="22" Background="RosyBrown">AAA</TextBox>
<TextBox Height="22" Background="Honeydew" Grid.Column="1">BBB</TextBox>
<Rectangle Fill="Khaki" Grid.Column="2"></Rectangle>

<GridSplitter Grid.Column="1" Width="4" Foreground="Red" HorizontalAlignment="Left" Background="Red"></GridSplitter>

</Grid>