• Torus Quotients of Homogeneous Spaces of the General Linear Group and the Standard Representation of Certain Symmetric Groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/119/01/0081-0100

• # Keywords

$GIT$ quotient; line bundle; simple reflection.

• # 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 $GL_{n+1}(k)/B_{n+1}$.

• # Author Affiliations

1. Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur Post Office, Siruseri 603 103, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019