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Enhanced adjoint
actions and their orbits for the general linear group
Kyo Nishiyama and Takuya Ohta |
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Vol. 298 (2019), No. 1, 141–155
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DOI: 10.2140/pjm.2019.298.141
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Abstract |
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We study an enhanced adjoint action of the general linear group on a product of its Lie algebra and a vector space consisting of several copies of defining representations and its duals. We determine regular semisimple orbits (i.e., closed orbits of maximal dimension) and the structure of enhanced null cone, including its irreducible components and their dimensions. |
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Keywords
enhanced nilpotent cone, exotic nilpotent cone, adjoint
quotient, classical invariant theory
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Mathematical Subject Classification 2010
Primary: 14L30
Secondary: 15A72, 16W22
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Milestones
Received: 19 March 2018
Accepted: 6 June 2018
Published: 2 February 2019
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Authors |
| Kyo Nishiyama | |
| Department of Physics and
Mathematics Aoyama Gakuin University Sagamihara Japan |
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| Takuya Ohta | |
| Depertment of Mathematics Tokyo Denki University Adachi-ku Japan |
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