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There is a special routine which computes the character table of
the alternating group, as well as routines which compute values of alternating
characters and the characters themselves. These routines make use of the fact
that in most cases the irreducible characters of the symmetric group,
which can be computed quickly, are also irreducible in the alternating
group. So the irreducible characters of the alternating
group may be indexed by partitions in the same way as those of
the symmetric group.
As the restriction of the irreducible character indexed by the
partition λ is equal to the restriction of the character
indexed by the conjugate partition, we only need to take one from each of these
pairs of partitions to form a full set of irreducible characters.
When a partition is conjugate to itself the character of the symmetric group
indexed by that partition is no longer irreducible but is the sum of two
irreducibles.
This method is described in [JK81].
Return the value of the character of the alternating group of degree n
indexed by the partition pa of weight n on the permutation pe.
The partition pa and its conjugate should be distinct.
Return the value of the ith character of the alternating group of degree n
indexed by the self conjugate partition pa of weight n on the permutation
pe. Since there are two possible irreducible characters indexed by such
partitions i must be either 1 or 2.
Return the character of the alternating group of degree n indexed by
the partition pa of weight n. The partition pa and its conjugate
should be distinct.
Return the ith character of the alternating group of degree n indexed
by the self conjugate partition pa of weight n.
Since there are two possible irreducible characters indexed by such partitions
i must be either 1 or 2.
Returns the character table of the alternating group of degree d.
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