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Mat. Sb., 2012, Volume 203, Number 3, Pages 127–160 (Mi msb7837)  

This article is cited in 3 scientific papers (total in 4 papers)

Representations of $\mathfrak{S}_\infty$ admissible with respect to Young subgroups

N. I. Nessonov

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: Let $\mathbb N$ be the set of positive integers and $\mathfrak S_\infty$ the set of finite permutations of $\mathbb N$. For a partition $\Pi$ of the set $\mathbb N$ into infinite parts $\mathbb A_1,\mathbb A_2, …$ we denote by $\mathfrak S_\Pi$ the subgroup of $\mathfrak S_\infty$ whose elements leave invariant each of the sets $\mathbb A_j$. We set $\mathfrak S_\infty^{(N)}= \{s\in \mathfrak S_\infty : s(i)=i for any i=1,2,…,N\}$. A factor representation $T$ of the group $\mathfrak S_\infty$ is said to be $\Pi$-admissible if for some $N$ it contains a nontrivial identity subrepresentation of the subgroup $\mathfrak S_\Pi\cap\mathfrak S_\infty^{(N)}$. In the paper, we obtain a classification of the $\Pi$-admissible factor representations of $\mathfrak S_\infty$.
Bibliography: 14 titles.

Keywords: factor representation, Young subgroup, $\Pi$-admissible representation.

DOI: https://doi.org/10.4213/sm7837

Full text: PDF file (775 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:3, 424–458

Bibliographic databases:

UDC: 517.986
MSC: Primary 20C32; Secondary 20B30
Received: 28.12.2010 and 12.05.2011

Citation: N. I. Nessonov, “Representations of $\mathfrak{S}_\infty$ admissible with respect to Young subgroups”, Mat. Sb., 203:3 (2012), 127–160; Sb. Math., 203:3 (2012), 424–458

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Yu. A. Neretin, “Infinite symmetric groups and combinatorial constructions of topological field theory type”, Russian Math. Surveys, 70:4 (2015), 715–773  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. E. Slyusarchuk, “Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$”, Sb. Math., 208:2 (2017), 255–268  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. J. Math. Sci. (N. Y.), 232:2 (2018), 138–156  mathnet  crossref
    4. A. M. Borodin, Aleksandr I. Bufetov, Aleksei I. Bufetov, A. M. Vershik, V. E. Gorin, A. I. Molev, V. F. Molchanov, R. S. Ismagilov, A. A. Kirillov, M. L. Nazarov, Yu. A. Neretin, N. I. Nessonov, A. Yu. Okounkov, L. A. Petrov, S. M. Khoroshkin, “Grigori Iosifovich Olshanski (on his 70th birthday)”, Russian Math. Surveys, 74:3 (2019), 555–577  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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