This paper is the second part of our study on limiting behavior of characters of wreath products $\mathfrak{S}_n(T)$
of compact group $T$
as $n\to\infty$
and its connection with characters of $\mathfrak{S}_\infty(T)$
. Contrasted with the first part, which has a representation-theoretical flavor, the approach of this paper is based on probabilistic (or ergodic-theoretical) methods. We apply boundary theory for a fairly general branching graph of infinite valencies to wreath products of an arbitrary compact group $T$
. We show that any character of $\mathfrak{S}_\infty(T)$
is captured as a limit of normalized irreducible characters of $\mathfrak{S}_n(T)$
as $n\to\infty$
along a path on the branching graph of $\mathfrak{S}_\infty(T)$
. This yields reconstruction of an explicit character formula for $\mathfrak{S}_\infty(T)$
.
Publié le : 2008-10-15
Classification:
the infinite symmetric group,
character,
factor representation,
wreath product,
probabilistic method,
20C32,
20P05,
20E22
@article{1225894038,
author = {HORA, Akihito and HIRAI, Takeshi and HIRAI, Etsuko},
title = {Limits of characters of wreath products },
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 1187-1217},
language = {en},
url = {http://dml.mathdoc.fr/item/1225894038}
}
HORA, Akihito; HIRAI, Takeshi; HIRAI, Etsuko. Limits of characters of wreath products . J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 1187-1217. http://gdmltest.u-ga.fr/item/1225894038/