Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSO(2n+1, C)

S. S. Kannan ; P. Saha

Journal of Lie theory, Tome 29 (2019) no. 1, pp. 107-142

Résumé

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.

Détail

Classification : 14M15
Mots-clés : Bott-Samelson-Demazure-Hansen variety, Coxeter element, tangent bundle