"Any $L^+G$-orbit in Gr is known to be an orbit of the form Oλ for some λ ∈ $X_*(T)$, and Oλ = Oμ iff λ and μ are conjugate by W and the orbits form a finite stratification of each of the $Gr_i$." who can prove this sentence? please tell me.

I also want to know the information $L^+T$-orbit in Gr and LN-orbit in Gr ,where T is max torus and N=[B,B],(B is a borel group )