Abstract:Let G be a reductive algebraic group in classical types A, B, D and e be an element of its Lie algebra with Z its centraliser in G for the adjoint action. We suppose that e identifies with an nilpotent matrix of order two, which guarantees the number of Z-orbits in the flag variety of G is finite. For types B, D in characteristic two, we also suppose the image of e is totally isotropic. We show that any closure Y of such orbit is normal. We also prove that Y is Cohen-Macaulay with rational singularities provid… Show more
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