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Induced representations of the infinite symmetric group and their spectral theory. (English. Russian original) Zbl 1327.20010

Dokl. Math. 75, No. 1, 1-4 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 412, No. 1, 7-10 (2007).
From the text: We formulate the main facts on the representations of the infinite symmetric group induced from the identity representations of Young subgroups. In particular, we describe when these representations are irreducible or factor representations, and give examples of computing their spectral measures.
For details see the authors’ paper [Pure Appl. Math. Q. 3, No. 4, 1005-1026 (2007; Zbl 1153.20008)].

MSC:

20C32 Representations of infinite symmetric groups
05E10 Combinatorial aspects of representation theory
22D30 Induced representations for locally compact groups

Citations:

Zbl 1153.20008
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References:

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