Abstract:
A complete list of indecomposable characters of the infinite symmetric semigroup is given. In comparison with a similar list for the infinite symmetric group, only one new parameter appears, which has a clear combinatorial meaning. The results rely on the representation theory of finite symmetric semigroups and the representation theory of the infinite symmetric group.
Citation:
A. M. Vershik, P. P. Nikitin, “Description of the Characters and Factor Representations of the Infinite Symmetric Inverse Semigroup”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 16–30; Funct. Anal. Appl., 45:1 (2011), 13–24
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\by A.~M.~Vershik, P.~P.~Nikitin
\paper Description of the Characters and Factor Representations of the Infinite Symmetric Inverse Semigroup
\jour Funktsional. Anal. i Prilozhen.
\yr 2011
\vol 45
\issue 1
\pages 16--30
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\jour Funct. Anal. Appl.
\yr 2011
\vol 45
\issue 1
\pages 13--24
\crossref{https://doi.org/10.1007/s10688-011-0002-0}
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Linking options:
https://www.mathnet.ru/eng/faa3023
https://doi.org/10.4213/faa3023
https://www.mathnet.ru/eng/faa/v45/i1/p16
This publication is cited in the following 10 articles:
P. Nikitin, N. Safonkin, “Semifinite harmonic functions on the direct product of graded graphs”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye metody. XXXIV, Zap. nauchn. sem. POMI, 517, POMI, SPb., 2022, 125–150
Jonas Wahl, “Traces on diagram algebras II: centralizer algebras of easy groups and new variations of the Young graph”, Algebraic Combinatorics, 5:3 (2022), 413
N. A. Safonkin, “Semifinite Harmonic Functions on Branching Graphs”, J Math Sci, 261:5 (2022), 669
N. A. Safonkin, “Semifinite harmonic functions on branching graphs”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye metody. XXXIII, Zap. nauchn. sem. POMI, 507, POMI, SPb., 2021, 114–139
N. I. Nessonov, “Characters of the Infinite Symmetric Inverse Semigroup”, Funct. Anal. Appl., 54:3 (2020), 179–187
Vershik A.M., “Asymptotic theory of path spaces of graded graphs and its applications”, Jap. J. Math., 11:2 (2016), 151–218
Vershik A., “Smoothness and Standardness in the Theory of AF-Algebras and in the Problem on Invariant Measures”, Probability and Statistical Physics in St. Petersburg, Proceedings of Symposia in Pure Mathematics, 91, eds. Sidoravicius V., Smirnov S., Amer Mathematical Soc, 2016, 423–436
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Petrov L., “Sl(2) Operators and Markov Processes on Branching Graphs”, J. Algebr. Comb., 38:3 (2013), 663–720
L. V. Bogachev, S. M. Zarbaliev, “Limit theorems for a certain class of random convex polygonal lines”, Russian Math. Surveys, 54:4 (1999), 830–832
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