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.
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, Tome 29 (2019) no. 1, pp. 107-142. http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a4/
@article{JOLT_2019_29_1_a4,
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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a4/}
}
TY - JOUR
AU - S. Senthamarai Kannan
AU - Pinakinath Saha
TI - Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSO(2n+1, C)
JO - Journal of Lie Theory
PY - 2019
SP - 107
EP - 142
VL - 29
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a4/
ID - JOLT_2019_29_1_a4
ER -
%0 Journal Article
%A S. Senthamarai Kannan
%A Pinakinath Saha
%T Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSO(2n+1, C)
%J Journal of Lie Theory
%D 2019
%P 107-142
%V 29
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2019_29_1_a4/
%F JOLT_2019_29_1_a4
