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arXiv · 2007.04110

On tangent cones to Schubert varieties in type $E$

Mikhail V. Ignatyev·Aleksandr A. Shevchenko
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Abstract

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.

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Mikhail V. Ignatyev, Aleksandr A. Shevchenko. 2020-07-07. On tangent cones to Schubert varieties in type $E$. https://arxiv.org/abs/2007.04110

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