Geodesic
On tangent cones to Schubert varieties in type $E$
Communications in Mathematics, Tome 28 (2020) no. 2, pp. 179-197.

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We consider tangent cones to Schubert subvarieties of the flag variety $G/B$, where $B$ is a Borel subgroup of a reductive complex algebraic group $G$ of type $E_6$, $E_7$ or $E_8$. We prove that if $w_1$ and $w_2$ form a good pair of involutions in the Weyl group $W$ of $G$ then the tangent cones $C_{w_1}$ and $C_{w_2}$ to the corresponding Schubert subvarieties of $G/B$ do not coincide as subschemes of the tangent space to $G/B$ at the neutral point.
Classification : 14M15, 17B22
Keywords: flag variety; Schubert variety; tangent cone; involution in the Weyl group; Kostant-Kumar polynomial 
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     author = {Ignatyev, Mikhail V. and Shevchenko, Aleksandr A.},
     title = {On tangent cones to {Schubert} varieties in type $E$},
     journal = {Communications in Mathematics},
     pages = {179--197},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2020},
     mrnumber = {4162929},
     zbl = {07300189},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2020__28_2_a6/}
}
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Ignatyev, Mikhail V.; Shevchenko, Aleksandr A. On tangent cones to Schubert varieties in type $E$. Communications in Mathematics, Tome 28 (2020) no. 2, pp. 179-197. http://geodesic.mathdoc.fr/item/COMIM_2020__28_2_a6/