Abstract
A theorem on the structure of the algebra of invariants of the commutant of a group generated by pseudoreflections is improved. In particular, it is shown that this algebra is a complete intersection. A series of counterexamples to Stanley's conjecture is constructed in dimension 4. Results supporting this conjecture for primitive groups of large dimension are given.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 120–130, 1982.
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Gordeev, N.L. Invariants of linear groups generated by matrices with two nonunit eigenvalues. J Math Sci 27, 2919–2927 (1984). https://doi.org/10.1007/BF01410744
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DOI: https://doi.org/10.1007/BF01410744