On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group

2011/07/04 by Petrov, Leonid
#05E05 #20C32 #60C05 #60J10 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1107.0676

Abstract

The z-measures on partitions originated from the problem of harmonic analysis of linear representations of the infinite symmetric group in the works of Kerov, Olshanski and Vershik (1993, 2004). A similar family corresponding to projective representations was introduced by Borodin (1997). The latter measures live on strict partitions (i.e., partitions with distinct parts), and the z-measures are supported by all partitions. In this note we describe some combinatorial relations between these two families of measures using the well-known doubling of shifted Young diagrams.

Related

• Z-measures on partitions related to the infinite Gelfand pair (S(2∞),H(∞))
• Probability measures on families of partitions related to harmonic analysis on big wreath products
• Random partitions and asymptotic theory of symmetric groups, Hecke algebras and finite Chevalley groups
• Character factorisations, z-asymmetric partitions and plethysm
• Induced Representations of Infinite Symmetric Group