Invariants of orthogonal \(G\)-modules from the character table. (English) Zbl 0978.20004

Nebe, Gabriele

Exp. Math. 9, No. 4, 623-629 (2000).

For a finite group \(G\) any \(\mathbb{Q} G\)-module \(V\) is uniquely determined by its character \(\chi_V\). Let \(q\) be a \(G\)-invariant quadratic form on \(V\). In the paper practical methods are developed to obtain information on the quadratic space \(\varphi=(V,q)\) and on the Clifford algebra \(C(\varphi)\) from the character \(\chi_V\). Several examples are given to illustrate the method.

Reviewer: Kanat Abdukhalikov (Dortmund)

MSC:

20C10	Integral representations of finite groups
20C15	Ordinary representations and characters
11E88	Quadratic spaces; Clifford algebras
15A63	Quadratic and bilinear forms, inner products
15A66	Clifford algebras, spinors

Keywords:

finite groups; characters; integral representations; Clifford algebras; quadratic forms

Software:

GAP

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