Rosas Celis, Mercedes Helena2024-02-062024-02-062019-12-08Rosas Celis, M.H. (2019). A comment of the combinatorics of the vertex operator Γ(t|X). Rocky Mountain Journal of Mathematics, 49 (7), 2281-2295. https://doi.org/10.1216/RMJ-2019-49-7-2281.0035-7596https://hdl.handle.net/11441/154706The Jacobi--Trudi identity associates a symmetric function to any integer sequence. Let Γ(t|X) be the vertex operator defined by Γ(t|X)sα=∑n∈Zs(n,α)[X]tn. We provide a combinatorial proof for the identity Γ(t|X)sα=σ[tX]sα[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.application/pdf14 p.engBernstein creation operatorscombinatorial aspect of representation theoryVertex operatorscombinatoricsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1216/RMJ-2019-49-7-2281