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ORBITS, RINGS OF INVARIANTS AND WEYL GROUPS FOR CLASSICAL Theta-GROUPS

机译:经典θ-群的轨道,不变环和Weyl群

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摘要

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.
机译:在本文中,我们研究了经典情况下Viberg Theta群的不变性理论。对于自然包含在一般线性组中的经典Theta-组,我们显示出限制图,从一般线性组的Lie代数的不变环到由Theta-组定义的Theta-表示的环。结果,我们获得了Theta表示不变环的代数独立的生成器。我们还给出了经典Theta-基团的Weyl基团的描述。

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