Log-Concavity of Multiplicities with Application to Characters ofU(∞)☆

The log-concavity of the reduction multiplicities for the classical groups of typeAn,Bn,Cnis proved, moreover the skew Schur functionssλ/μare shown to be log-concave coefficient by coefficient. The results are applied to the calculation of the characters of the infinite-dimensional classical groups. The log-concavity of density of the push-forward of the Liouville measure on coadjoint orbits under moment map is proved.

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