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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.

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    $\begingroup$ What kind of description would you expect? $\endgroup$
    – Sasha
    Jan 17, 2021 at 19:24
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    $\begingroup$ Perhaps you can add some definitions (blow-up space, the quotient $G/B$, etc). Also, what do you mean by "description"? An intuitive explanation of the technical definition, perhaps? $\endgroup$ Jan 17, 2021 at 21:11
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    $\begingroup$ Thanks for considering MO. This question could do with a bit more detail, in particular, as noted on the help box "1. Summarize the problem. 2. Provide details and any research. 3.When appropriate, describe what you’ve tried" It's hard for people to know what sort of answer is appropriate if they do not know what your background is. Writing a bit more about how this problem arose in your work gives reasonable context that people can then adapt to. $\endgroup$
    – David Roberts
    Jan 17, 2021 at 23:00
  • $\begingroup$ Actually, I am looking for the description of the Blow-up space of $G/B$ at $B$ using embedding of $G/B$ inside some projective space associated to a dominant character of $B.$ And also How the $B$ action lifts to this space. I want to study How automorphism group of this space is related to that of $G/B.$ My Background in algebraic geometry is not very good and references related to this will also be very helpful. $\endgroup$ Jan 18, 2021 at 17:20
  • $\begingroup$ The automorphism group of the blow up is just the subroup of $\operatorname{Aut}(G/B) $ preserving the point $B$ (in particular it contains $B$). $\endgroup$
    – abx
    Jan 20, 2021 at 6:57

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