Journal of the Mathematical Society of Japan

Upper triangular parts of conjugacy classes of nilpotent matrices with finite number of $B$-orbits


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We consider the intersection of the conjugacy class of a nilpotent matrix with the space of upper triangular matrices. We give necessary and sufficient conditions for this intersection to be a union of finitely many orbits for the action by conjugation of the group of invertible upper triangular matrices.

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J. Math. Soc. Japan, Volume 65, Number 3 (2013), 967-992.

First available in Project Euclid: 23 July 2013

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Zentralblatt MATH identifier

Primary: 17B08: Coadjoint orbits; nilpotent varieties
Secondary: 20G99: None of the above, but in this section 05E10: Combinatorial aspects of representation theory [See also 20C30]

nilpotent matrices nilpotent orbits spherical varieties orbital varieties


FRESSE, Lucas. Upper triangular parts of conjugacy classes of nilpotent matrices with finite number of $B$-orbits. J. Math. Soc. Japan 65 (2013), no. 3, 967--992. doi:10.2969/jmsj/06530967.

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