Let V be a finite dimensional vector space over a field K of characteristic / 2, and b: the orthogonal group of b. Another orthogonal representation Ε½ . Ε½ . Π: G Βͺ O bΠ is orthogonally equiΒ¨alent to if there is an isometry : Ε½ . VΒͺVΠwhich commutes with the action of G, i.e., satisfies bΠ u, Ε½ . sb
Equivalence of Absolutely Irreducible Orthogonal Representations of Finite Groups
β Scribed by C. Riehm
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 177 KB
- Volume
- 181
- Category
- Article
- ISSN
- 0021-8693
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β¦ Synopsis
Let V be a finite dimensional vector space over a field K of characteristic / 2, and b: V = V Βͺ K a non-degenerate symmetric bilinear form.
Ε½ . Let : G Βͺ O b be an orthogonal representation of the finite group G. Unless mentioned otherwise, we assume throughout that is absolutely irreducible as a linear representation. We wish to investigate the orthogo-X * Support by N.S.E.R.C. Grant 5-36724 gratefully acknowledged. 601
π SIMILAR VOLUMES
Let V be a finite dimensional vector space over a field K of characteristic / 2, and b: the orthogonal group of b. Another orthogonal representation Ε½ . Ε½ . Π: G Βͺ O bΠ is orthogonally equiΒ¨alent to if there is an isometry : Ε½ . VΒͺVΠwhich commutes with the action of G, i.e., satisfies bΠ u, Ε½ . sb
We describe an algorithmic test, using the "standard polynomial identity" (and elementary computational commutative algebra), for determining whether or not a finitely presented associative algebra has an irreducible n-dimensional representation. When n-dimensional irreducible representations do exi