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The Virtual Poincaré Polynomials of Homogeneous Spaces

Published online by Cambridge University Press:  04 December 2007

Michel Brion  and
Emmanuel Peyre
Michel Brion
Affiliation:
Université de Grenoble I, Département de Mathématiques, Institut Fourier, UMR 5582 du CNRS, 38402 Saint-Martin D'Hères Cedex, France. e-mail: michel.brion@ujf-grenoble.fr
Emmanuel Peyre
Affiliation:
Université de Grenoble I, Département de Mathématiques, Institut Fourier, UMR 5582 du CNRS, 38402 Saint-Martin D'Hères Cedex, France. e-mail: emmanuel.peyre@ujf-grenoble.fr
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Abstract

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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.

Keywords

homogeneous spacesvirtual Poincaré polynomials
Type
Research Article
Information
Compositio Mathematica , Volume 134 , Issue 3 , December 2002 , pp. 319 - 335
Copyright
© 2002 Kluwer Academic Publishers