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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc804919 |
| Date | 08 1900 |
| Creators | Berardinelli, Angela |
| Contributors | Douglass, J. Matthew, Shepler, Anne V., Brozovic, Douglas |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 31 pages : illustration, Text |
| Rights | Public, Berardinelli, Angela, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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