Polynomiality of Subdimensions of Diagonal Harmonics and a Sharp Stability Bound

Xinxuan Wang

A sequence of $S_n$-representations $\{V_n{\}}_{n\ge 1}$ is representation stable if, writing $V(\lambda )=(n-|\lambda |,{\lambda }_1,{\lambda }_2,\dots )$ for each partition $\lambda$, the multiplicity of the irred…