Irreducible characters with equal roots in the groups S n and A n
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We show that treating of (non-trivial) pairs of irreducible characters of the group Sn sharing the same set of roots on one of the sets An and Sn \ An is divided into three parts. This, in particular, implies that any pair of such characters χα and χβ (α and β are respective partitions of a number n) possesses the following property: lengths d(α) and d(β) of principal diagonals of Young diagrams for α and β differ by at most 1.
Keywordsgroup irreducible character Young diagram
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- 6.G. James, The Representation Theory of the Symmetric Groups, Lect. Notes Math., Vol. 682, Springer (1978).Google Scholar