Zonal polynomials and domino tableaux (Q1191936)

Let \(H\) be a subgroup of a finite group \(G\). One can define the idempotent element \(\theta\) of the group algebra \({\mathcal A}(G)\) by \(\theta=\Sigma_{h\in H}h/| H|\). If \((H,G)\) is a Gelfand pair then the decomposition of \(\theta\) into minimal idempotents yields a basis for the Hecke algebra \({\mathcal H}(H,G)\). The authors prove that the Fourier transform of the minimal idempotents is supported by standard domino tableaux. Moreover, they present a multiplication algorithm for zonal polynomials and relate the expansion coefficients to the Littlewood-Richardson's coefficients.