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Ignatyev, Mikhail V.; Shevchenko, Aleksandr A.

On tangent cones to Schubert varieties in type \(E\). (English) Zbl 1460.14110

Commun. Math. 28, No. 2, 179-197 (2020).
Summary: 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.

MSC:

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

Keywords:

flag variety; Schubert variety; tangent cone; involution in the Weyl group; Kostant-Kumar polynomial

Software:

SageMath
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References:

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