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Journal of the London Mathematical Society 2003 68(2):461-476; doi:10.1112/S0024610703004472
© 2003 by London Mathematical Society
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© The London Mathematical Society

Affine Twin Buildings

Mark Ronan

Mathematics Department, University of Illinois 851 S. Morgan, mc249, Chicago, IL 60607, USA

Received 28 June 2002. Revision received 28 November 2002.

It is well known from work of Bruhat and Tits that an affine building has a spherical building at infinity. The paper studies the structure at infinity for an affine twin building. It is shown that the twinning restricts the structure at infinity in a natural way, producing two smaller spherical buildings that are canonically isomorphic to one another. In the process it is shown that to each wall and panel of these buildings at infinity is attached a twin tree.


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