Article ID Journal Published Year Pages File Type
4583724 Journal of Algebra 2016 28 Pages PDF
Abstract

We study tangent cones to Schubert subvarieties of the flag variety of a complex reductive group G. Let T be a maximal torus of G, B be a Borel subgroup of G containing T, Φ be the root system of G with respect to T, W   be the Weyl group of Φ, and F=G/BF=G/B be the flag variety. We prove that if every irreducible component of Φ is of type BnBn or CnCn, and w1w1, w2w2 are two distinct involutions in W  , then the tangent cones at the point p=eBp=eB to the corresponding Schubert subvarieties Xw1Xw1, Xw2Xw2 of FF do not coincide as subschemes of the tangent space TpFTpF. We also show that if every irreducible component of Φ is of type AnAn or CnCn, then the reduced tangent cones to Xw1Xw1 and Xw2Xw2 do not coincide as subvarieties of TpFTpF.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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