Edges and tableaux. (Arêtes et tableaux.)
Relative dimensions of isotypic components of th order tensor representations of the symmetric group on letters give a Plancherel-type measure on the space of Young diagrams with cells and at most rows. It was conjectured by G. Olshanski that dimensions of isotypic components of tensor representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to this family of Plancherel-type measures in the limit when converges to a constant. The main...