\def\C{{\Bbb C}} Let $G=PSp(2n, \C)$ ($n\ge 3$) and $B$ be a Borel subgroup of $G$ containing a maximal torus $T$ of $G$. Let $w$ be an element of the 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 groups 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 $\underline i$ of $w_0$ in terms of a Coxeter element such that all the higher cohomology groups of the tangent bundle on $Z(w_0, \underline i)$ vanish.
1
Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India
B. Narasimha Chary; S. Senthamarai Kannan. Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C). Journal of Lie Theory, Tome 27 (2017) no. 2, pp. 435-468. http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a7/
@article{JOLT_2017_27_2_a7,
author = {B. Narasimha Chary and S. Senthamarai Kannan},
title = {Rigidity of {Bott-Samelson-Demazure-Hansen} {Variety} for {PSp(2n,} {C)}},
journal = {Journal of Lie Theory},
pages = {435--468},
year = {2017},
volume = {27},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a7/}
}
TY - JOUR
AU - B. Narasimha Chary
AU - S. Senthamarai Kannan
TI - Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C)
JO - Journal of Lie Theory
PY - 2017
SP - 435
EP - 468
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a7/
ID - JOLT_2017_27_2_a7
ER -
%0 Journal Article
%A B. Narasimha Chary
%A S. Senthamarai Kannan
%T Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C)
%J Journal of Lie Theory
%D 2017
%P 435-468
%V 27
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a7/
%F JOLT_2017_27_2_a7
