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Linear representation theory of symmetric group:S3

178 bytes added, 17:28, 23 February 2013
Relation with representations of subgroups
===Relationship between irreducibles and those of subgroups: Frobenius reciprocity===
Here, the rows correspond to irreducible representations of the whole group, and the columns correspond to irreducible representations of the subgrop. The number in a cell is the multiplicity of the column representation in the restriction of the row representation to the subgroup; equivalently, it is the multiplicity of the row representation in the [[induced representation]] from the column representation of the subgroup to the whole group. These numbers are equal by [[Frobenius reciprocity]].
Between the whole group and its 3-Sylow subgroup:
===Verification of the McKay conjecture===
The [[McKay conjecture ]] needs to be verified for primes 2 and 3. Since the 3-Sylow subgroup is normal, nothing needs to be checked for 3. The 2-Sylow subgroup is self-normalizing. The two numbers are:
# The number of odd-dimensional characters of the symmetric group: This is 2.
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