Reduced Kronecker Coefficients and Counter–Examples to Mulmuley’s Strong Saturation Conjecture SH: With an Appendix by Ketan Mulmuley

摘要: We provide counter–examples to Mulmuley’s strong saturation conjecture (strong SH) for the Kronecker coefficients. This was proposed in setting of Geometric Complexity Theory show that deciding whether or not a coefficient is zero can be done polynomial time. also short proof #P– hardness computing Both results rely on connections between coefficients and another family structural constants representation theory symmetric groups, Murnaghan’s reduced coefficients. An appendix by Mulmuley introduces relaxed form hypothesis SH, still enough aims Theory.