On Characters of Finite Groups by Michel Broué

Author:Michel Broué
Language: eng
Format: epub
ISBN: 9789811068782
Publisher: Springer Singapore

The next theorem uses the Frobenius–Schur indicator defined in 3.​2.​29.

Theorem 4.2.20

Let S be an irreducible -module with character . In each item (1), (2), (3), assertions (i), (ii) and (iii) are equivalent.

(1) (i) (R) holds.

(ii) There is a symmetric nondegenerate bilinear form on S invariant under G.

(iii)

(2) (i) (C) holds.

(ii) There is no nonzero bilinear form on S invariant under G.

(iii)

(3) (i) (H) holds.

(ii) There is an alternating bilinear form on S invariant under G.

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