B-orbits of 2-nilpotent matrices and generalizations

Details B-orbits of 2-nilpotent matrices and generalizations B-orbits of 2-nilpotent matrices and generalizations

2010-04-12

arxiv.org/abs/1004.1996v1

Mathematics

Representation Theory

20 pages, 1 figure

Scientific paper

The orbits of the group B of upper-triangular matrices acting on 2-nilpotent complex matrices via conjugation are classified via oriented link patterns, generalizing A. Melnikov's classification of the B-orbits on upper-triangular such matrices. The orbit closures as well as the "building blocks" of minimal degenerations of orbits are described. The classification uses the theory of representations of finite-dimensional algebras. Furthermore, we initiate the study of the B-orbits on arbitrary nilpotent matrices.

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