A fixed point formula of Lefschetz type in Arakelov geometry III: representations of Chevalley schemes and heights of flag varieties |
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| Authors: | Christian Kaiser Kai Köhler |
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| Institution: | (1) Mathematisches Institut, Wegelerstr. 10, D-53115 Bonn, Germany (e-mail: ck@math.uni-bonn.de), DE;(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 |
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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.
Oblatum 17-VI-1999 & 10-IX-2001?Published online: 19 November 2001 |
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| Keywords: | Mathematical Subject Classification (2000): 14G40 58J52 20G05 20G10 14M17 |
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