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Certain unitary representations of the infinite symmetric group, II

Published online by Cambridge University Press:  22 January 2016

Nobuaki Obata
Nobuaki Obata*
Affiliation:
Department of Mathematics, Faculty of Science Nagoya University, Chikusa-ku, Nagoya, 464, Japan
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The infinite symmetric group is the discrete group of all finite permutations of the set X of all natural numbers. Among discrete groups, it has distinctive features from the viewpoint of representation theory and harmonic analysis. First, it is one of the most typical ICC-groups as well as free groups and known to be a group of non-type I. Secondly, it is a locally finite group, namely, the inductive limit of usual symmetric groups . Furthermore it is contained in infinite dimensional classical groups GL(ξ), O(ξ) and U(ξ) and their representation theories are related each other.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 106 , June 1987 , pp. 143 - 162
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

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