Restricting Invariants and Arrangements of Finite Complex Reflection Groups

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Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of C-invariant functions on X. In my thesis, I extend earlier work by Douglass and Röhrle for Coxeter groups to the case where G is a complex reflection group of type G(r,p,n) in the notation of Shephard and Todd and X ... continued below

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iv, 31 pages : illustration

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Berardinelli, Angela August 2015.

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  • Berardinelli, Angela

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Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of C-invariant functions on X. In my thesis, I extend earlier work by Douglass and Röhrle for Coxeter groups to the case where G is a complex reflection group of type G(r,p,n) in the notation of Shephard and Todd and X is in the lattice of the reflection arrangement of G. The main result characterizes when the restriction mapping is surjective in terms of the exponents of G and C and their reflection arrangements.

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iv, 31 pages : illustration

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  • August 2015

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  • March 4, 2016, 4:14 p.m.

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  • April 19, 2017, 8:02 a.m.

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Berardinelli, Angela. Restricting Invariants and Arrangements of Finite Complex Reflection Groups, dissertation, August 2015; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc804919/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .