Stretched Newell–Littlewood coefficients

Newell-Littlewood coefficients $n_{\mu,\nu}^{\lambda}$ are the multiplicities occurring in decomposition of products universal characters orthogonal and symplectic groups. They may also be expressed, or even defined directly terms Littlewood-Richardson coefficients, $c_{\mu,\nu}^{\lambda}$. Both sets have stretched forms $c_{t\mu,t\nu}^{t\lambda}$ $n_{t\mu,t\nu}^{t\lambda}$, where $t\kappa$ is partition obtained by multiplying each part $\kappa$ integer $t$. It known that a polynomial $t$ here it shown $n_{t\mu,t\nu}^{t\lambda}$ an Ehrhart quasi-polynomial with minimum quasi-period at most $2$. The evaluation effected both deriving their generating function establishing hive model analogous to used for calculation $c_{t\mu,t\nu}^{t\lambda}$. These two approaches lead whole battery conjectures about nature quasi-polynomials $n_{t\mu,t\nu}^{t\lambda}$. include positivity, stability saturation supported significant amount data from range examples.