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Young subgroup

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Let be a partition of into disjoint subsets. Then the corresponding Young subgroup of , the symmetric group on letters, is the subgroup

where . Sometimes only the particular cases

are meant where , where and is a partition of the natural number , i.e. , .

References

[a1] G.D. James, "The representation theory of the symmetric groups" , Springer (1978) pp. 13
[a2] A. Kerber, "Representations of permutation groups" , I , Springer (1971) pp. 17
How to Cite This Entry:
Young subgroup. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Young_subgroup&oldid=19253