Journal of Lie Theory

no. 2
Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C)
Journal of Lie Theory, Volume 27 (2017) no. 2, pp. 435-468
\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.
DOI: 10.5802/jolt.954
Classification: 14F17, 14M15
Keywords: Bott-Samelson-Demazure-Hansen variety, Coxeter element, tangent bundle 
@article{JOLT_2017_27_2_a7,
     author = {B. N. Chary and S. S. 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},
     doi = {10.5802/jolt.954},
     zbl = {1429.14014},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.954/}
}
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%A S. S. Kannan
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%J Journal of Lie Theory
%D 2017
%P 435-468
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%R 10.5802/jolt.954
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B. N. Chary; S. S. Kannan. Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C). Journal of Lie Theory, Volume 27 (2017) no. 2, pp. 435-468. doi: 10.5802/jolt.954

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