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We construct a compactification $\\phi:T^*G/P\\rightarrow X(u)$, where $X(u)$ is a Schubert variety corresponding to the loop group $LG$. Let $N^*X(w)\\subset T^*G/P$ be the conormal variety of some Schubert variety $X(w)$ in $G/P$; hence we obtain that the closure of $\\phi(N^*X(w))$ in $X(u)$ is a $B$-stable compactification of $N^*X(w)$. 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