2011/07/08 by Mkrtchyan, Sevak
#05D40 #05E10 #20C30 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1107.1541
Relative dimensions of isotypic components of N-th order tensor representations of the symmetric group on n letters give a Plancherel-type measure on the space of Young diagrams with n cells and at most N 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 N/sqrtn converges to a constant. The main result of the paper is the proof of this conjecture.