Number of components of the nullcone
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 95-101.

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For every pair $(G,V)$ where $G$ is a connected simple linear algebraic group and $V$ is a simple algebraic $G$-module with a free algebra of invariants, the number of irreducible components of the nullcone of unstable vectors in $V$ is found.
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V. L. Popov. Number of components of the nullcone. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 95-101. http://geodesic.mathdoc.fr/item/TRSPY_2015_290_a7/

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