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Simplicial complexes lying equivariantly over the affine building of GL(N)

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Abstract.

Let G=GL(N,K), K a non-archimedean local field and X be the semisimple affine building of G over K. We construct a projective tower of G-sets with X(0)=X. They are obtained by using a minor modification in Bruhat and Tits’ original construction (an idea due to P. Schneider). Using the structure of X as an abstract building, we construct a projective tower of simplicial G-complexes such that, for each r, X (r) is canonically a geometrical realization of X r . In the case N=2, X r has a natural two-sheeted covering r and we show that the supercuspidal part of the cohomology space is characterized by a nice property.

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Authors and Affiliations

  1. UMR6086 CNRS, SP2MI - Téléport 2, Bd M. et P. Curie, 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Paul Broussous

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  1. Paul Broussous
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Correspondence to Paul Broussous.

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Mathematics Subject Classification (2000): 14R25, 20E42, 20G25, 55U10, 57S25

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Broussous, P. Simplicial complexes lying equivariantly over the affine building of GL(N). Math. Ann. 329, 495–511 (2004). https://doi.org/10.1007/s00208-004-0516-3

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  • DOI: https://doi.org/10.1007/s00208-004-0516-3

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