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A fixed point formula of Lefschetz type in Arakelov geometry III: representations of Chevalley schemes and heights of flag varieties

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Abstract.

We give a new proof of the Jantzen sum formula for integral representations of Chevalley schemes over Spec Z, except for three exceptional cases. This is done by applying the fixed point formula of Lefschetz type in Arakelov geometry to generalized flag varieties. Our proof involves the computation of the equivariant Ray-Singer torsion for all equivariant bundles over complex homogeneous spaces. Furthermore, we find several explicit formulae for the global height of any generalized flag variety.

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Authors and Affiliations

  1. Mathematisches Institut, Wegelerstr. 10, D-53115 Bonn, Germany (e-mail: ck@math.uni-bonn.de), , , , , , DE

    Christian Kaiser

  2. Centre de Mathématiques de Jussieu, C.P. 7012, 2, place Jussieu, F-75251 Paris Cedex 05, France (e-mail: koehler@math.jussieu.fr/ http://www.math.jussieu.fr/~koehler), , , , , , FR

    Kai Köhler

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  1. Christian Kaiser
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  2. Kai Köhler
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Oblatum 17-VI-1999 & 10-IX-2001¶Published online: 19 November 2001

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Kaiser, C., Köhler, K. A fixed point formula of Lefschetz type in Arakelov geometry III: representations of Chevalley schemes and heights of flag varieties. Invent. math. 147, 633–669 (2002). https://doi.org/10.1007/s002220100187

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  • DOI: https://doi.org/10.1007/s002220100187

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