Separating invariants and finite reflection groups |
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Authors: | Emilie Dufresne |
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Affiliation: | Department of Mathematics and Statistics, Queen's University, Jeffery Hall, University Avenue, Kingston, ON, Canada, K7L 3N6 |
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Abstract: | A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras. |
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Keywords: | Invariant theory Separating invariants Finite groups Reflections Polynomial ring Bireflections Complete intersection ring |
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