期刊论文详细信息
Proceedings Mathematical Sciences
Torus Quotients of Homogeneous Spaces of the General Linear Group and the Standard Representation of Certain Symmetric Groups
S S Kannan2  Pranab Sardar1 
[1] $$;Chennai Mathematical Institute, Plot H, SIPCOT IT Park, Padur Post Office, Siruseri 0 0, India$$
关键词: $GIT$ quotient;    line bundle;    simple reflection.;   
DOI  :  
学科分类:数学(综合)
来源: Indian Academy of Sciences
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【 摘 要 】

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 $GL_{n+1}(k)/B_{n+1}$.

【 授权许可】

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