The invariant theory of finite reflection groups has rich connections to geometry, topology, representation theory, and combinatorics. We consider finite reflection groups acting on vector spaces over fields of arbitrary characteristic, where many arguments of classical invariant theory break down. When the characteristic of the underlying field is positive, reflections may be nondiagonalizable. A group containing these so-called transvections has order which is divisible by the characteristic of the underlying field, so is in the modular setting. In this thesis, we examine the action on differential derivations, which include products of differential forms and derivations, and identify the structure of the set of invariants under the action of groups fixing a single hyperplane, groups with maximal transvection root spaces acting on vector spaces over prime fields, as well as special linear groups and general linear groups over finite fields.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc2137649 |
| Date | 05 1900 |
| Creators | Hanson, Dillon James |
| Contributors | Shepler, Anne, Schmidt, Ralf, Conley, Charles |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Hanson, Dillon James, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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