Journal of Lie Theory 27 (2017), No. 2, 435--468
Copyright Heldermann Verlag 2017
Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C)
B. Narasimha Chary
Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India
chary@cmi.ac.in
S. Senthamarai Kannan
Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India
kannan@cmi.ac.in
[Abstract-pdf]
\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.
Keywords: Bott-Samelson-Demazure-Hansen variety, Coxeter element, tangent bundle.
MSC: 14F17, 14M15
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