Journal of Lie Theory

no. 1
Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSO(2n+1, C)
S. Senthamarai Kannan1; Pinakinath Saha1
1Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India
Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 107-142
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.
DOI: 10.5802/jolt.1050
Classification: 14M15
Keywords: Bott-Samelson-Demazure-Hansen variety, Coxeter element, tangent bundle

S. Senthamarai Kannan  1 ; Pinakinath Saha  1

1 Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India 
S. Senthamarai Kannan; Pinakinath Saha. Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSO(2n+1, C). Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 107-142. doi: 10.5802/jolt.1050
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     author = {S. Senthamarai Kannan and Pinakinath Saha},
     title = {Rigidity of {Bott-Samelson-Demazure-Hansen} {Variety} for {PSO(2n+1,} {C)}},
     journal = {Journal of Lie Theory},
     pages = {107--142},
     year = {2019},
     volume = {29},
     number = {1},
     doi = {10.5802/jolt.1050},
     zbl = {1415.14016},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1050/}
}
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