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Characters of Finite Groups
New Features:
- A utility RationalCharacterTable has been installed to compute the
table of rational characters
of a finite group. Note that it is the character values that are rational.
These characters will be afforded by rational representations if and only if
the appropriate Schur index is 1. The algorithm starts by computing the
character table of the given group.
- An algorithm has been implemented for computing the p-blocks of
the table of ordinary characters for a finite group.
The algorithm used is very fast once the table of ordinary characters has been
constructed. It relies on computing inner products over p-regular elements of
the group. The computations are performed in a finite field for speed.
The intrinsic function is named Blocks. Another utility
DefectGroup will return a defect group of a p-block.
Bug Fixes:
- The intrinsic function CharacterTable now applies to
finite groups of type GrpAb. A serious memory problem when computing
the characters of an abelian group has also been fixed.
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