RÉSUMÉ

Let G be a finite group. Any Q G-module V is uniquely determined by its character chi_V. So in principle chi_V also determines the G-invariant quadratic forms on V.
Invariants for a non-degenerate quadratic space phi := (V,q) over an arbitrary field K can be read off from the Clifford algebra C(phi). This is a Z/2Z-graded algebra functorially attached to phi and it determines the two most important invariants of the quadratic space phi : its determinant and its Clifford invariant. If G acts on phi = (V,q) as isometries, then G acts on C(phi) as algebra automorphisms respecting the grading. From this observation, character theoretic methods are developed to determine the rational isometry classes of the G-invariant quadratic forms. There are other methods to calculate these isometry classes among which induced representations play an important role. I present an orthogonal version of Frobenius reciprocity that allows to deal with such representations.

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