Hoeffding spaces and Specht modules

Giovanni Peccati , Jean-Renaud Pycke

It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

Mots clés: Exchangeability; finite population statistics; Hoeffding decompositions; irreducible representations; random permutations; Specht modules; symmetric group

Giovanni Peccati, Jean-Renaud Pycke. Hoeffding spaces and Specht modules. ESAIM: Probability and Statistics, 2010, 15, pp.S58-S68. ⟨10.1051/ps/2010022⟩. ⟨hal-00632717⟩