Orbits, rings of invariants and Weyl groups for classical $\Theta$-groups

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概要

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• In this paper, we study the invariant theory of Viberg's $\Theta$-groups in classical cases. For a classical $\Theta$-group naturally contained in a general linear group, we show the restriction map, from the ring of invariants of the Lie algebra of the general linear group to that of the $\Theta$-representation defined by the $\Theta$-group, is surjective. As a consequence, we obtain explicitly algebraically independent generators of the ring of invariants of the $\Theta$-representation. We also give a description of the Weyl groups of the classical $\Theta$-groups.

著者

• Ohta Takuya

  Department Of Mathematics Tokyo Denki University

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