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1 results

  • The Virtual Poincaré Polynomials of Homogeneous Spaces

  • Michel Brion, Emmanuel Peyre
  • Journal:
    Compositio Mathematica / Volume 134 / Issue 3 / December 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 319-335
    Print publication:
    December 2002
    • Article
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  • 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 $t^{2u} (t^2-1)^r Q_{G/H}(t^2)$ for a polynomial $Q_{G/H}$ with nonnegative integer coefficients. Moreover, we show that $Q_{G/H}(t^2)$ divides the virtual Poincaré polynomial of every regular embedding of G/H, if H is connected.