Difference operators for partitions under the Littlewood decomposition
Résumé
The concept of t-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure , based on walks in the Young lattice with steps given by the addition of t-hooks. It is well-known that the hook lengths of multiples of t can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo t.
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