On the centralizer of the sum of commuting nilpotent elements

Details On the centralizer of the sum of commuting nilpotent elements On the centralizer of the sum of commuting nilpotent elements

2004-12-14

arxiv.org/abs/math/0412283v2

Journal of Pure and Applied Algebra. Volume 206, Issues 1-2, July 2006, Pages 123-140. Special issue dedicated to Eric M. Frie

Mathematics

Representation Theory

12 pages. To appear in the Friedlander birthday volume of J. Pure and Applied Algebra

Scientific paper

10.1016/j.jpaa.2005.04.016

Let X and Y be commuting nilpotent K-endomorphisms of a vector space V, where K is a field of characteristic p >= 0. If F=K(t) is the field of rational functions on the projective line, consider the K(t)-endomorphism A=X+tY of V. If p=0, or if the (p-1)-st power of A is 0, we show here that X and Y are tangent to the unipotent radical of the centralizer of A in GL(V). For all geometric points (a:b) of a suitable open subset of the projective line, it follows that X and Y are tangent to the unipotent radical of the centralizer of aX+bY. This answers a question of J. Pevtsova.

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