Tuesday, November 9
Matt Zaremsky, University of Virginia
In recent work with Peter Abramenko, we have exhibited two large classes of group actions on buildings that are Weyl transitive but not strongly transitive with respect to any apartment system. The first class of examples arises by inspecting torsion properties in Chevalley groups. The other, more recent results involve analyzing division algebras, with the conclusion that for any central F-division algebra D of degree greater than 2, the action of the norm-1 or multiplicative group on the associated building is "not even close" to being strongly transitive. For certain fields F, we can exhibit such actions that are nonetheless Weyl transitive.
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