Teor. Veroyatn. Primen.,

English translation: Prob. Theory Appl.,

**Abstract.**
We show that the class of so-called Markov representations of
the infinite symmetric group, associated with Markov
measures on the space of infinite Young tableaux, coincides
with the class of simple representations, i.e., inductive
limits of representations with simple spectrum.
The spectral measure of an arbitrary representation of the infinite symmetric group
with simple spectrum is equivalent to a multi-Markov measure
on the space of Young tableaux.
We also show that the representations of the infinite symmetric group
induced from the
identity representations of two-block
Young subgroups are Markov and find explicit formulas
for the transition probabilities of the corresponding Markov measures.
The induced representations are studied with the help of the tensor
model of two-row representations of the symmetric groups;
in particular, we deduce explicit formulas for the Gelfand-Tsetlin basis
in the tensor models.

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