A comment of the combinatorics of the vertex operator Γ_(t|X) [article]

Mercedes Helena Rosas
2017 arXiv   pre-print
The Jacobi--Trudi identity associates a symmetric function to any integer sequence. Let Γ_(t|X) be the vertex operator defined by Γ_(t|X) s_α =∑_n ∈Z s_(n,α) [X] t^n. We provide a combinatorial proof for the identity Γ_(t|X) s_α = σ[tX] s_α[x-1/t] due to Thibon et al. We include an overview of all the combinatorial ideas behind this beautiful identity, including a combinatorial description for the expansion of s_(n,α) [X] in the Schur basis, for any integer value of n.
arXiv:1701.02516v2 fatcat:dhnahbee5zfldfphrxvsdrvfea