Tame automorphisms of the free nilpotent groups and property T

The group of tame automorhisms of the free nilpotent group consists of
those automorphisms that are induced from the covering free group.
By a theorem of Lubotzky and Pak, these groups have property T whenever
the number of generators exceeds two.

In this talk, we will compute some Kazhdan constants for these groups that
in turn give rise to effective bounds for the mixing time of product
replacement random walk on finite nilpotent groups.