Abstract
The orbits of the group B n of upper-triangular matrices acting on 2-nilpotent complex matrices via conjugation are classified via oriented link patterns, generalizing Melnikov’s classification of the B n -orbits on upper-triangular such matrices. The orbit closures and 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 n -orbits on arbitrary nilpotent matrices.
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Acknowledgements
The authors would like to thank K. Bongartz and A. Melnikov for valuable discussions concerning the methods and results of this work.
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Boos, M., Reineke, M. (2012). B-Orbits of 2-Nilpotent Matrices and Generalizations. In: Joseph, A., Melnikov, A., Penkov, I. (eds) Highlights in Lie Algebraic Methods. Progress in Mathematics, vol 295. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8274-3_6
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DOI: https://doi.org/10.1007/978-0-8176-8274-3_6
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