Uniform ${\mathcal{C}}^k$ Approximation of $G$-Invariant and Antisymmetric Functions, Embedding Dimensions, and Polynomial Representations

Soumya Ganguly, Khoa Tran, Rahul Sarkar

For any subgroup $G$ of the symmetric group ${\mathcal{S}}_n$ on $n$ symbols, we present results for the uniform ${\mathcal{C}}^k$ approximation of $G$-invariant functions by $G$-invar…