67.24 InducedAction

InducedAction( module, basis )
SubGModule( module, basis )
QuotientGModule( module, basis )

These functions take a G-module module as input, together with a basis basis for a proper submodule, which is assumed to be normalised, in the weak sense that the first non-zero component of each vector in the basis is 1, and no two vectors in the basis have their first nonzero components in the same position. The basis is given as an r times n matrix, where r is the length of the basis.

Normally, one runs IsIrreducible(module) first, and (assuming it returns false) then runs these functions using SubbasisFlag(module) as the second argument. InducedAction returns a 4-element list containing the submodule, the quotient module, the original matrices rewritten with respect to a basis in which a basis for the submodule comes first, and the change-of-basis matrix; SubGModule returns the submodule having basis as basis; QuotientGModule the corresponding quotient module.

RandomIrreducibleSubGModule( module )

Find a basis for an irreducible submodule of module.

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