Vol. 298, No. 1, 2019

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Enhanced adjoint actions and their orbits for the general linear group

Kyo Nishiyama and Takuya Ohta

Vol. 298 (2019), No. 1, 141–155
DOI: 10.2140/pjm.2019.298.141
Abstract

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
Mathematical Subject Classification 2010
Primary: 14L30
Secondary: 15A72, 16W22
Milestones
Received: 19 March 2018
Accepted: 6 June 2018
Published: 2 February 2019
Authors
Kyo Nishiyama
Department of Physics and Mathematics
Aoyama Gakuin University
Sagamihara
Japan
Takuya Ohta
Depertment of Mathematics
Tokyo Denki University
Adachi-ku
Japan