Representations of S{sub {infinity}} admissible with respect to Young subgroups
- B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov (Ukraine)
Let N be the set of positive integers and S{sub {infinity}} the set of finite permutations of N. For a partition {Pi} of the set N into infinite parts A{sub 1},A{sub 2},... we denote by S{sub {Pi}} the subgroup of S{sub {infinity}} whose elements leave invariant each of the sets A{sub j}. We set S{sub {infinity}}{sup (N)}={l_brace}s element of S{sub {infinity}:} s(i)=i for any i=1,2,...,N{r_brace}. A factor representation T of the group S{sub {infinity}} is said to be {Pi}-admissible if for some N it contains a nontrivial identity subrepresentation of the subgroup S{sub {Pi}} intersection S{sub {infinity}}{sup (N)}. In the paper, we obtain a classification of the {Pi}-admissible factor representations of S{sub {infinity}}. Bibliography: 14 titles.
- OSTI ID:
- 21612779
- Journal Information:
- Sbornik. Mathematics, Vol. 203, Issue 3; Other Information: DOI: 10.1070/SM2012v203n03ABEH004229; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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