Restricting Invariants and Arrangements of Finite Complex Reflection Groups Metadata

Metadata describes a digital item, providing (if known) such information as creator, publisher, contents, size, relationship to other resources, and more. Metadata may also contain "preservation" components that help us to maintain the integrity of digital files over time.

Title

  • Main Title Restricting Invariants and Arrangements of Finite Complex Reflection Groups

Creator

  • Author: Berardinelli, Angela
    Creator Type: Personal

Contributor

  • Chair: Douglass, J. Matthew
    Contributor Type: Personal
    Contributor Info: Major Professor
  • Committee Member: Shepler, Anne V.
    Contributor Type: Personal
  • Committee Member: Brozovic, Douglas
    Contributor Type: Personal

Publisher

  • Name: University of North Texas
    Place of Publication: Denton, Texas
    Additional Info: www.unt.edu

Date

  • Creation: 2015-08

Language

  • English

Description

  • Content Description: 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.
  • Physical Description: iv, 31 pages : illustration

Subject

  • Keyword: mathematics
  • Keyword: algebra
  • Keyword: invariant theory
  • Keyword: reflection groups
  • Library of Congress Subject Headings: Invariants.
  • Library of Congress Subject Headings: Finite groups.
  • Library of Congress Subject Headings: Reflection groups.

Collection

  • Name: UNT Theses and Dissertations
    Code: UNTETD

Institution

  • Name: UNT Libraries
    Code: UNT

Rights

  • Rights Access: public
  • Rights Holder: Berardinelli, Angela
  • Rights License: copyright
  • Rights Statement: Copyright is held by the author, unless otherwise noted. All rights Reserved.

Resource Type

  • Thesis or Dissertation

Format

  • Text

Identifier

  • Archival Resource Key: ark:/67531/metadc804919

Degree

  • Academic Department: Department of Mathematics
  • Degree Discipline: Mathematics
  • Degree Level: Doctoral
  • Degree Name: Doctor of Philosophy
  • Degree Grantor: University of North Texas
  • Degree Publication Type: disse

Note