An integral transform for p-adic symmetric spaces, by Peter Schneider and Jeremy Teitelbaum

This paper has appeared in Duke Math. J. 86, (1997), no. 3, 391 - 433, and so the dvi version has been removed. Earlier work of Schneider and Stuhler showed that the top dimensional deRham cohomology of Drinfeld's d-dimensional p-adic symmetric space X over a complete local field K of characteristic zero is isomorphic to the dual of the Steinberg representation of G=GL(d+1,K). In this paper, we construct an explicit map from the dual of Steinberg to the space of top dimensional differential forms on X. This isomorphism is obtained by integrating an appropriate kernel function over G/B(K).

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Peter Schneider <pschnei@math.uni-muenster.de>
Jeremy Teitelbaum <jeremy@math.uic.edu>