Hoeffding spaces and Specht modules

2009/04/20 by Peccati, Giovanni, Pycke, Jean-Renaud
#05E10 #60C05 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.0904.3086

Abstract

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.

Related

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• Vertices of Specht modules and blocks of the symmetric group
• On C-bases, partition pairs and filtrations for induced or restricted Specht modules
• Large Dimension Homomorphism Spaces Between Specht Modules for Symmetric Groups
• Specht Modules for Weyl Groups