Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups

We give a stratification of the GIT quotient of the Grassmannian G2,n modulo the normaliser of a maximal torus of SLn(k) with respect to the ample generator of the Picard group of G2,n. We also prove that the flag variety GLn(k)/Bn can be obtained as a GIT quotient of GLn+1(k)/Bn+1 modulo a maximal torus of SLn+1(k) for a suitable choice of an ample line bundle on GLn+1(k)/Bn+1.