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Let $n\in\mathbb N$ be a natural number and $\lambda=(a,b)\vdash n$ a partition of $n$ into two parts, i.e. $a\ge b$ and $a+b=n$. In this special case, is there a simple description of the character $\chi_\lambda$ of the irreducible $S_n$-representation corresponding to $\lambda$? I have tried to deduce something from the Frobenius character formula and also using the Murnaghan-Nakayama recursion, but so far I couldn't really come up with a simple description. I would really appreciate any references/theorems in that direction.

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I think this is what you want, but it's just a link, so I just leave it as a comment: ma.rhul.ac.uk/~uvah099/Maths/labels.pdf –  Aaron Mar 5 '13 at 17:05
    
Unfortunately, I don't see how that helps me =/. –  user38451 Mar 5 '13 at 17:30
    
Sorry, it's my bad, he only have a formula relating characters for permutation module and Specht module of tow rows partition there...I think it's worth to try to ask this question on Mathoverflow instead if you don't get good answer within a week time. –  Aaron Mar 5 '13 at 20:44

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