Geodesic
Kostant--Kumar polynomials and tangent cones to Schubert varieties for involutions in $A_n$, $F_4$ and $G_2$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 82-105

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Let $G$ be a complex reductive algebraic group and $W$ its Weyl group. We prove that if $W$ are of type $A_n$, $F_4$ or $G_2$ and $w,w'$ are disjoint involutions in $W$, then the corresponding Kostant–Kumar polynomials do not coincide. As a consequence, we deduce that the tangent cones to the Schubert subvarieties $X_w$, $X_{w'}$ of the flag variety of $G$ do not coincide, too. 
@article{ZNSL_2013_414_a4,
     author = {D. Yu. Eliseev and M. V. Ignat'ev},
     title = {Kostant--Kumar polynomials and tangent cones to {Schubert} varieties for involutions in $A_n$, $F_4$ and $G_2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--105},
     publisher = {mathdoc},
     volume = {414},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a4/}
}
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D. Yu. Eliseev; M. V. Ignat'ev. Kostant--Kumar polynomials and tangent cones to Schubert varieties for involutions in $A_n$, $F_4$ and $G_2$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 82-105. http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a4/