Abstract
It is shown that there are finitely many irreducible finite-dimensional orthogonal modules V (up to isomorphism) over any complex simple Lie algebras such that Spin0(V) is decomposably-generated in the sense of Panyushev [The exterior algebra and "Spin" of an orthogonal 𝔤-module, Trans. Groups6 (2001) 371–396]. The case of simple Lie algebras of type A is discussed.
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