The Molecular Species $\mathbf{C}_α$: Geometric Realization and a Closed Formula for Kronecker Coefficients

Abstract: In this paper we first introduce the \emph{infinite multi-row periodic pattern of shape $α$} as a geometric realization of $\mathbf{C}<em>α$. We then give an explicit formula for the coefficients $b^λ</em>{α,β}$ appearing in the species decomposition [ \mathbf{C}α\times \mathbf{C}β = \sum_{λ\vdash n} b^λ{α,β}\,\mathbf{C}λ. ]