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

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

2007-08-16

arxiv.org/abs/0708.2138v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

We give a stratification of the GIT quotient of the Grassmannian $G_{2,n}$ modulo the normaliser of a maximal torus of $SL_{n}(k)$ with respect to the ample generator of the Picard group of $G_{2,n}$. We also prove that the flag variety $GL_{n}(k)/B_{n}$ can be obtained as a GIT quotient of $GL_{n+1}(k)/B_{n+1}$ modulo a maximal torus of $SL_{n+1}(k)$ for a suitable choice of an ample line bundle on $GL_{n+1}(k)/B_{n+1}$.

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