The Virtual Poincaré Polynomials of Homogeneous Spaces |
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| Authors: | Michel Brion Emmanuel Peyre |
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| Institution: | (1) Département de Mathématiques, Institut Fourier, UMR 5582 du CNRS, Université de Grenoble I, 38402 Saint-Martin D'Hères Cedex, France;(2) Département de Mathématiques, Institut Fourier, UMR 5582 du CNRS, Université de Grenoble I, 38402 Saint-Martin D'Hères Cedex, France |
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| Abstract: | We factor the virtual Poincaré polynomial of every homogeneous space G/H, where G is a complex connected linear algebraic group and H is an algebraic subgroup, as t2u (t2–1)r QG/H(t2) for a polynomial QG/H with nonnegative integer coefficients. Moreover, we show that QG/H(t2) divides the virtual Poincaré polynomial of every regular embedding of G/H, if H is connected. |
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| Keywords: | homogeneous spaces virtual Poincaré polynomials |
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