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SUMMARY:Buildings of type \\tilde{A}_n and the growth of the natural cocyc
le for the Steinberg representation
DTSTART;VALUE=DATE-TIME:20141127T130000
DTEND;VALUE=DATE-TIME:20141127T140000
UID:c381fba7172cbf35acba8d5ca788accef1478d11c297cdbca43cf6ac
CATEGORIES:Conferences - Seminars
DESCRIPTION:In this talk\, I will try to present some basics about Euclide
an buildings and explain the topic of my Ph.D. thesis. Buildings are very
complicated structures\; to simplify the picture\, we will keep in mind a
building of type \\tilde{A}_n. Those buildings are modelled on the Euclide
an space \\mathbb{R}^n tessellated by equilateral n-tetrahedrons. I will b
riefly explain how one gets a building from a (B\,N)-pair of a group. The
most famous such example is the building of Bruhat and Tits associated to
the group SL_{n+1}(F) where F is a non-archimedean local field\, say \\mat
hbb{Q}_p. Such groups have a unitarisable representation "St"\, the so-cal
led the Steinberg representation\, which is of cohomological interest\, an
d a natural cocycle "Vol". The latter is a geometrically defined map that
sends an n-tuple of points in the building to a vector in St. The aim of m
y thesis is to compute the growth of the norm of these vectors as the poin
ts get far away from each other inside the building. If time permits\, I w
ill present the case n=1\, in which case the building is the (p+1)-regular
tree T and the cocycle Vol is the Busemann cocycle of T. Here\, the squar
e of the norm grows at most linearly with the distance between two points.
LOCATION:MA A 3 31 http://plan.epfl.ch/?room=MA%20A3%2031
STATUS:CONFIRMED
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