Journal of Lie Theory 29 (2019), No. 1, 107--142
Copyright Heldermann Verlag 2019
Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSO(2n+1, C)
S. Senthamarai Kannan
Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India
kannan@cmi.ac.in
Pinakinath Saha
Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India
pinakinath@cmi.ac.in
[Abstract-pdf]
Let $G=PSO(2n+1, \mathbb{C})$ $(n \ge 3)$ and $B$ be the Borel subgroup of $G$ containing maximal torus $T$ of $G.$ Let $w$ be an element of Weyl group $W$ and $X(w)$ be the Schubert variety in the flag variety $G/B$ corresponding to $w.$ Let $Z(w, \underline{i})$ be the Bott-Samelson-Demazure-Hansen Variety (the desingularization of $X(w)$) corresponding to a reduced expression $\underline{i}$ of $w.$\par In this article, we study the cohomology modules of the tangent bundle on $Z(w_{0}, \underline{i}),$ where $w_{0}$ is the longest element of the Weyl group $W.$ We describe all the reduced expressions of $w_{0}$ in terms of a Coxeter element such that all the higher cohomology modules of the tangent bundle on $Z(w_{0}, \underline{i})$ vanish.
Keywords: Bott-Samelson-Demazure-Hansen variety, Coxeter element, tangent bundle.
MSC: 14M15
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