Orbits, rings of invariants and Weyl groups for classical $\Theta$-groups
Ohta, Takuya
Tohoku Math. J. (2), Tome 62 (2010) no. 1, p. 527-558 / Harvested from Project Euclid
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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.
Publié le : 2010-05-15
Classification:  17B70,  13A50,  14R20 
@article{1294170345,
     author = {Ohta, Takuya},
     title = {Orbits, rings of invariants and Weyl groups for classical $\Theta$-groups},
     journal = {Tohoku Math. J. (2)},
     volume = {62},
     number = {1},
     year = {2010},
     pages = { 527-558},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1294170345}
}

Ohta, Takuya. Orbits, rings of invariants and Weyl groups for classical $\Theta$-groups. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp.  527-558. http://gdmltest.u-ga.fr/item/1294170345/