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Note on a Theorem of Eng
Victor Reiner
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
reiner@math.umn.edu
Annals of Combinatorics 6 (1) p.117-118 March, 2002
AMS Subject Classification: 20F55
Abstract:
A theorem of O. Eng on the Poincare polynomial of parabolic quotients of finite Coxeter groups evaluated at -1 is given a case-free geometric proof for Weyl groups.
Keywords: Coxeter group, Poincare polynomial, parabolic quotient, generalized flag manifold, q=-1 phenomenon

References:

1. Connolly and Nagano, The intersection pairing of a homogeneous Kˇ§ahler manifold, Mich. Math. J. 24 (1977) 33¨C39.

2. O. Eng, Quotients of Poincar¨¦ polynomials evaluated at --1, J. Algebraic Combin. 13 (2001) 29¨C40.

3. P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1994.

4. H. Hiller, Geometry of Coxeter Groups, Research Notes in Mathematics 54, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982.

5. R.O.Wells, Differential Analysis on Complex Manifolds, Second Edition, Graduate Texts in Math. 65, Springer-Verlag, New York-Berlin, 1980.