Rigidity of Bott-Samelson-Demazure-Hansen variety for F₄ and G₂ · arXivDesk1908.05595Aug 13, 201946 pages. arXiv admin note: text overlap with arXiv:1610.00812, arXiv:1908.05605
Rigidity of Bott-Samelson-Demazure-Hansen variety for F4 and G2
S. Senthamarai Kannan, Pinakinath Saha
Abstract
Let G be a simple algebraic group of adjoint type over C, whose root system is of type F4. Let T be a maximal torus of G
and
be a Borel subgroup of
containing
Let
be an element of Weyl group
and
be the Schubert variety in the flag variety
corresponding to
Let
Z(w,i) be the Bott-Samelson-Demazure-Hansen variety (the desingularization of
) corresponding to a reduced expression
of
In this article, we study the cohomology modules of the tangent bundle on
Z(w0,i), where
is the longest element of the Weyl group
We describe all the reduced expressions of
in terms of a Coxeter element such that
Z(w0,i) is rigid (see Theorem 8.1). Further, if
is of type
there is no reduced expression
of
for which
Z(w0,i) is rigid (see Theorem 8.2).