Robinson-Schensted-Knuth insertion and characters of symmetric groups and Iwahori-Hecke algebras of type A

1996/07/05 by Ram, Arun · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/9607231

Abstract

The purpose of this note is to give an insertion scheme proof of the formula, p_μ= ∑_{λ\vdash k} χ^λ(μ)s_λ,\formula where p_μ is the power sum symmetric function, s_λ is the Schur function and χ^λ(μ) is the irreducible character of the symmetric group S_k indexed by the partition λ and evaluated at a permutation of cycle type μ=(μ₁,…,μ_ℓ). The proof of this formula is by direct application of the Robinson-Schensted-Knuth insertion scheme and a recent formula of Roichman.

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