Survey of Jordan types for pairs of commuting nilpotent matrices, including review of the proof of the Box Conjecture.
Jordan types commuting with a hook partition
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abstract
We give a complete classification of the Jordan types occurring in the nilpotent commutator of a nilpotent matrix whose Jordan type is a hook partition. As a consequence, we also show that two partitions with the same generic commuting Jordan type need not commute with each other.
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math.AC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Jordan types for pairs of commuting nilpotent matrices: A survey
Survey of Jordan types for pairs of commuting nilpotent matrices, including review of the proof of the Box Conjecture.