Is there somewhere I can read about the spherical building at infinity for $SL(n, \mathbb{Q}_p)$?
I'm looking for something with lots of explicit examples and computations. (I have books on the general theory, but these are hard for me to parse)
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1$\begingroup$ The spherical building itself is just a projective space, which is easy to understand. What exactly is it you would like to know? $\endgroup$– Tom De MedtsCommented Jan 11, 2017 at 10:01
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$\begingroup$ For example, for SL(3, Q_2), I know I need to glue together copies of the Heawood graph. Where can I find explicit examples/ computations like this for SL(n,Q_p) for other values of p and n? $\endgroup$– Arielle LeitnerCommented Jan 13, 2017 at 15:11
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$\begingroup$ I still don't completely understand the analogy with projective space $\endgroup$– Arielle LeitnerCommented Jan 13, 2017 at 15:12
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1 Answer
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For a treatment of buildings with examples (not only for the spherical building, but for other notions as well) I recommand :
Abramenko, Brown, Buildings, Theory and applications, GTM 248, Springer 2008
Dasgupta, Teitelbaum, The $p$-adic upper half plane, in $p$-adic geometry, Lect Ser. 45, AMS, 2008 (for the case of ${\rm SL}(2)$)
Garrett, Buildings and classical groups, Chapman & Hall, 1997.
Ronan, Buildings: main ideas and applications. I Main ideas Bull LMS 1992
Ronan, Buildings: main ideas and applications. II Arithmetic groups, buildings and symmetric spaces, Bull LMS 1992
answered Jan 11, 2017 at 12:38