What is the description of the blow-up space of $G/B$ at $B.$ Specifically:
(1) Can we describe it explicitly using an embedding of $G/B$ into some projective space associated to a dominant character of $B$?
(2) How does the action of $B$ lift to the blow-up of $G/B$ at $B$?
(3) How does the automorphism group of this blow-up relate to the automorphism group of $G/B$?
References related to this will also be very helpful.