• 1 Samara National Research University

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.

• 14M15 - Grassmannians, Schubert varieties, flag manifolds
• 17B08 - Coadjoint orbits; nilpotent varieties
• 20F55 - Reflection and Coxeter groups (group-theoretic aspects)