Pure Appl. Math. Quart.,

**Abstract.**
We study the representations of the infinite symmetric group induced
from the identity representations of Young subgroups. It turns out
that such induced representations
can be either of type I or of type II. Each Young subgroup corresponds
to a partition of the set of positive integers;
depending on the sizes of blocks of this partition, we divide Young subgroups
into two classes:
large and small subgroups.
The first class gives representations of type I, in particular, irreducible
representations. The most part of Young subgroups of
the second class give representations of type II and, in particular,
von Neumann factors of
type II. We present a number of various examples. The main
problem is to find the so-called spectral measure of the induced representation.
The complete solution of this problem is given for two-block Young subgroups
and subgroups with infinitely many singletons and finitely many finite blocks
of length greater than one.

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