Breaking down the reduced Kronecker coefficients

Abstract

We resolve three interrelated problems on \emph{reduced Kronecker coefficients} $\overline{g}(\alpha ,\beta ,\gamma )$. First, we disprove the \emph{saturation property} which states that $\overline{g}(N\alpha ,N\beta ,N\gamma )>0$ implies $\overline{g}(\alpha ,\beta ,\gamma )>0$ for all $N>1$. Second, we esimate the maximal $\overline{g}(\alpha ,\beta ,\gamma )$, over all $|\alpha |+|\beta |+|\gamma |=n$. Finally, we show that computing $\overline{g}(\lambda ,\mu ,\nu )$ is strongly $\#P$-hard, i.e. $\#P$-hard when the input $(\lambda ,\mu ,\nu )$ is in unary.

arXiv comment5 pages

References in corpus (5)

• Quantum marginal problem and representations of the symmetric group
• On Nonzero Kronecker Coefficients and their Consequences for Spectra
• The stability of the Kronecker products of Schur functions
• Reduced Kronecker coefficients and counter-examples to Mulmuley's strong saturation conjecture SH
• Upper bounds on Kronecker coefficients with few rows

Cited by in corpus (1)

• Upper bounds on Kronecker coefficients with few rows