Young Derivation of the Trace Cocharacters of the 2 × 2 Matrices

Here we show that the sequences of characters https://www.w3.org/1998/Math/MathML"> ϕ n = ∑ λ ∈ Λ 2 ( n ) χ λ ⊗ χ λ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332630/bdf2b6ad-8ca8-4d57-9bb0-ce1a8aabf4d0/content/inline-math296.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> Ω n = https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332630/bdf2b6ad-8ca8-4d57-9bb0-ce1a8aabf4d0/content/inline-math297.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> ∑ λ ∈ H ( 1 , 1 , ; n ) χ λ ⊗ χ λ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332630/bdf2b6ad-8ca8-4d57-9bb0-ce1a8aabf4d0/content/inline-math298.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> are Young-derived from simpler sequences. This yields the decomposition of φ _n to its irreducibles. The corresponding decomposition of Ω_n is given in [Rem].