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Abstract:
Let X,Y be commuting nilpotent nxn matrices, and
let t be
transcendental over the ground field k. If k has positive
characteristic p>0, we suppose also that (X+tY)p-1 = 0. Then for all
points (a:b) in a suitable open subset of the projective line, we show
that X and Y are both tangent to the unipotent radical of the
centralizer in GL(n) of aX + bY; this answers a question of
J. Pevtsova. The talk will describe this result. Moreover, I'll
describe why the result remains true for reductive groups which are
more general than GL(n) (under mild assumptions on the characteristic
of k). Finally, I'll try to discuss possible applications to the
nilpotent commuting variety.
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