Let G be a complex reductive algebraic group and W be its Weyl group. We prove that if W is of type An, F4, or G2 and w, w’ are disjoint involutions in W, then the corresponding Kostant–Kumar polynomials do not coincide. As a consequence, we deduce that the tangent cones to the Schubert subvarieties Xw, Xw’ of the flag variety of G do not coincide as well.
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To dear Professor Nikolai Vavilov with gratitude and admiration
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 414, 2013, pp. 82–105.
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Eliseev, D.Y., Ignatyev, M.V. Kostant–Kumar Polynomials and Tangent Cones to Schubert Varieties for Involutions in A n , F 4, and G 2 . J Math Sci 199, 289–301 (2014). https://doi.org/10.1007/s10958-014-1856-5
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DOI: https://doi.org/10.1007/s10958-014-1856-5