A proof of the Murnaghan–Nakayama rule by Specht modules and tableau combinatorics. / Kochhar, Jasdeep; Wildon, Mark.

In: Annals of combinatorics, 23.04.2019.

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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.
Original languageEnglish
Number of pages21
JournalAnnals of combinatorics
Publication statusAccepted/In press - 23 Apr 2019

ID: 33719598