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

      S S Kannan Pranab Sardar

      Volume 119 Issue 1 February 2009 pp 81-100

    • Fulltext

       

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      Permanent link:
      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

       

      S S Kannan1 Pranab Sardar1

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

    • Dates

       
      Published
      February 2009
      Manuscript received
      28 August 2007
      Manuscript revised
      28 December 2007

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