Stability of coefficients in the Kronecker product of a hook and a rectangle

摘要: We use recent work of Jonah Blasiak (2012 arXiv:1209.2018) to prove a stability result for the coefficients in Kronecker product two Schur functions: one indexed by hook partition and rectangle partition. also give nearly sharp bounds size starting with which are stable. Moreover, we show that once bound is reached, no new functions appear decomposition product. call this property superstability. Thus, can recover from smallest case superstability holds. The sharp. Our study particular motivated its usefulness understanding quantum Hall effect (Scharf T et al 1994 J. Phys. A: Math. Gen 27 4211–9).