Bureaucrats, emailconfirmed, Administrators

38,910

edits
Jump to: navigation, search

→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.

Retrieved from "https://groupprops.subwiki.org/wiki/Special:MobileDiff/45556"