I'd like an explanation of the term "HIGH ALPHA"? Does it stand for High Angle of attack? Also, in the harrier maneuver, is the wing stalled and the airplane hanging on the propeller?

Your correct both times. But I think you knew that.

A definition for High Alpha came to me as I was writing the question down. Given that there are two "A"s in "High Angles of Attack", the term should be referred to as "high alpha alpha"! However, I have a hard time believeing the wing is stalled in a Harrier maneuver. Without the wing providing some lift, why doesn't the nose drop?

Alpha is the Greek letter used in engineering to represent angle-of-attack in equations.

As for the harrier, I don't think anyone can say for 100% sure what the aero is. Even though your airspeed is low, the prop blast over the wing gives airspeed and lift over that section of the wing's surface. This may be the reason that the very low aspect ratio wings tend to harrier easily; they have a large portion of the wing "blown" by the prop. The majority of good 3D harrier planes have either a low aspect ratio or a wide root chord.

Thrust vectoring. The plane actually becomes a helicopter as it transfers from its stall speed to the props vectoring force.