GIT quotient of a Bott–Samelson–Demazure–Hansen variety by a maximal torus

S. S. Kannan*, J. F. Thomsen

*Corresponding author for this work

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Let G be an almost simple, simply connected algebraic group over the field C of complex numbers. Let B be a Borel subgroup of G containing a maximal torus T of G, and let W be the Weyl group defined by T. The Borel group B determines a subset of simple reflections in W. For w in W, we let Z(w,i̲) be the Bott–Samelson–Demazure–Hansen variety corresponding to a reduced expression i̲ of w as a product of these simple reflections. In this article, we study the geometric invariant theoretic quotient of Z(w,i̲) for the T-linearized ample line bundles.

Original languageEnglish
Article number25
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
Publication statusPublished - 2019


  • Bott–Samelson–Demazure–Hansen variety
  • line bundle
  • semi-stable points


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