Rigidity of Bott-Samelson-Demazure-Hansen Variety for PSp(2n, C)

B. N. Chary ; S. S. Kannan

Journal of Lie theory, Tome 27 (2017) no. 2, pp. 435-468

Résumé

\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.

Détail

Classification : 14F17, 14M15
Mots-clés : Bott-Samelson-Demazure-Hansen variety, Coxeter element, tangent bundle