Tohoku Mathematical Journal

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

Takuya Ohta

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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.

Article information

Tohoku Math. J. (2), Volume 62, Number 4 (2010), 527-558.

First available in Project Euclid: 4 January 2011

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Zentralblatt MATH identifier

Primary: 17B70: Graded Lie (super)algebras
Secondary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24] 14R20: Group actions on affine varieties [See also 13A50, 14L30]


Ohta, Takuya. Orbits, rings of invariants and Weyl groups for classical $\Theta$-groups. Tohoku Math. J. (2) 62 (2010), no. 4, 527--558. doi:10.2748/tmj/1294170345.

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