Entropy of Schur–Weyl measures

Sevak Mkrtchyan

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 2, page 678-713
  • ISSN: 0246-0203

Abstract

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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 n converges to a constant. The main result of the paper is the proof of this conjecture.

How to cite

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Mkrtchyan, Sevak. "Entropy of Schur–Weyl measures." Annales de l'I.H.P. Probabilités et statistiques 50.2 (2014): 678-713. <http://eudml.org/doc/271950>.

@article{Mkrtchyan2014,
abstract = {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 $\frac\{N\}\{\sqrt\{n\}\}$ converges to a constant. The main result of the paper is the proof of this conjecture.},
author = {Mkrtchyan, Sevak},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {asymptotic representation theory; Schur-Weyl duality; Plancherel measure; Schur-Weyl measure; Vershik-Kerov conjecture},
language = {eng},
number = {2},
pages = {678-713},
publisher = {Gauthier-Villars},
title = {Entropy of Schur–Weyl measures},
url = {http://eudml.org/doc/271950},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Mkrtchyan, Sevak
TI - Entropy of Schur–Weyl measures
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 2
SP - 678
EP - 713
AB - 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 $\frac{N}{\sqrt{n}}$ converges to a constant. The main result of the paper is the proof of this conjecture.
LA - eng
KW - asymptotic representation theory; Schur-Weyl duality; Plancherel measure; Schur-Weyl measure; Vershik-Kerov conjecture
UR - http://eudml.org/doc/271950
ER -

References

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