On tangent cones to Schubert varieties in type e Mikhail V. Ignatyev, Aleksandr A. Shevchenko Communications in Mathematics, 2020 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 Cw 1 and Cw 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.
On cones tangent to schubert varieties of type Dn M. V. Ignat′ev, A. A. Shevchenko St Petersburg Mathematical Journal, 2016 It is proved that the tangent cones to Schubert subvarieties of the flag variety of a reductive group with root system of type $D_n$ do not coincide if they correspond to different basic involutions in the Weyl group.
