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arXiv · 1712.08023

A recursion formula for the irreducible characters of the symmetric group

Randall R. Holmes
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Abstract

The branching theorem expresses irreducible character values for the symmetric group $S_n$ in terms of those for $S_{n-1}$, but it gives the values only at elements of $S_n$ having a fixed point. We extend the theorem by providing a recursion formula that handles the remaining cases. It expresses these character values in terms of values for $S_{n-1}$ together with values for $S_n$ that are already known in the recursive process. This provides an alternative to the Murnaghan-Nakayama formula.

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Randall R. Holmes. 2017-12-21. A recursion formula for the irreducible characters of the symmetric group. https://arxiv.org/abs/1712.08023

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