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arXiv · 0708.2138

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

S. S. Kannan·Pranab Sardar
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Abstract

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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S. S. Kannan, Pranab Sardar. 2007-08-16. Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups. https://arxiv.org/abs/0708.2138

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