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

S. S. Kannan; Pranab Sardar

paper

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

arXiv:0708.2138

Abstract

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

19 pages