B-orbits of 2-nilpotent matrices and generalizations

2010/04/12 by M. Boos, Markus Reineke, Boos, Magdalena +1
Computer Science · Engineering · Mathematics · #Advanced Research in Systems and Signal Processing #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1004.1996

openalex publication_date 2010/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• B-orbits of nilpotent order 2 and link patterns
• Parabolic orbits of 2-nilpotent elements for classical groups
• Conjugation on varieties of nilpotent matrices
• The Orbit Method for Finite Groups of Nilpotency Class Two of Odd Order
• Coadjoint orbits for A_n-1⁺, B_n⁺, and D_n⁺