## Tohoku Mathematical Journal

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

Takuya Ohta

#### Abstract

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

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

Dates
First available in Project Euclid: 4 January 2011

https://projecteuclid.org/euclid.tmj/1294170345

Digital Object Identifier
doi:10.2748/tmj/1294170345

Mathematical Reviews number (MathSciNet)
MR2768758

Zentralblatt MATH identifier
1242.17024

#### Citation

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. https://projecteuclid.org/euclid.tmj/1294170345

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