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Equivalence of Absolutely Irreducible Orthogonal Representations of Finite Groups

✍ 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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✦ 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


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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 . Ј: G Βͺ O bЈ is orthogonally equiΒ¨alent to if there is an isometry : Ε½ . VΒͺVЈwhich commutes with the action of G, i.e., satisfies bЈ u, Ε½ . sb

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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 . Ј: G Βͺ O bЈ is orthogonally equiΒ¨alent to if there is an isometry : Ε½ . VΒͺVЈwhich commutes with the action of G, i.e., satisfies bЈ u, Ε½ . sb

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