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arXiv · 1805.00255

A proof of the Murnaghan--Nakayama rule using Specht modules and tableau combinatorics

Jasdeep Kochhar·Mark Wildon
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Abstract

The Murnaghan--Nakayama rule is a combinatorial rule for the character values of symmetric groups. We give a new combinatorial proof by explicitly finding the trace of the representing matrices in the standard basis of Specht modules. This gives an essentially bijective proof of the rule. A key lemma is an extension of a straightening result proved by the second author to skew-tableaux. Our module theoretic methods also give short proofs of Pieri's rule and Young's rule.

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BibTeXRIS

Jasdeep Kochhar, Mark Wildon. 2018-05-01. A proof of the Murnaghan--Nakayama rule using Specht modules and tableau combinatorics. https://arxiv.org/abs/1805.00255

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