Semifinite harmonic functions on the direct product of graded graphs
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 125-150 Cet article a éte moissonné depuis la source Math-Net.Ru

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Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.
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P. Nikitin; N. Safonkin. Semifinite harmonic functions on the direct product of graded graphs. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 125-150. http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a7/

[1] N. A. Safonkin, “Semifinite harmonic functions on branching graphs”, Zap. Nauchn. Semin. POMI, 507, 2021, 114–139 | MR

[2] S. V. Kerov, A. M. Vershik, “Characters, factor representations and $K$-functor of the infinite symmetric group”, Operator algebras and group representations, v. II, 1980 | MR

[3] A. J. Wassermann, Automorphic actions of compact groups on operator algebras, Ph.D. thesis, University of Pennsylvania, 1981 https://repository.upenn.edu/dissertations/AAI8127086/ | MR

[4] G. Olshanski, “The problem of harmonic analysis on the infinite-dimensional unitary group”, J. Funct. Anal., 205:2 (2003), 464–524 | DOI | MR

[5] R. R. Phelps, Lectures on Choquet's theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966 | MR

[6] R. P. Boyer, “Infinite traces of AF-algebras and characters of ${\rm U}(\infty )$”, J. Operator Theory, 9:2 (1983), 205–236 | MR

[7] A. Borodin G. Olshanski, Representations of the infinite symmetric group, Cambridge University Press, Cambridge, 2017 | MR

[8] S. V. Kerov, “Combinatorial examples in the theory of AF-algebras”, Zap. Nauchn. Sem. LOMI, 172, 1989, 55–67, 169–170 | MR

[9] S. V. Kerov, Asymptotic representation theory of the symmetric group and its applications in analysis, Amer. Math. Soc., Providence, RI, 2003 | MR

[10] S. V. Kerov, A. M. Vershik, “The $K$-functor (Grothendieck group) of the infinite symmetric group”, Zap. Nauchn. Sem. LOMI, 123, 1983, 126–151 | MR

[11] A. Gnedin, G. Olshanski, “Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams”, Int. Math. Res. Not., 2006, 51968, 39 pp. | MR

[12] S. V. Kerov, A. M. Vershik, “Locally semisimple algebras. Combinatorial theory and the $K_0$-functor”, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, VINTI, M., 1985, 3–56 | MR

[13] Ş. Strătilă, D. Voiculescu, Representations of AF-algebras and of the group $U(\infty)$, Springer-Verlag, Berlin-New York, 1975 | MR

[14] O. Bratteli, Inductive Limits of Finite Dimensional $C^*$-Algebras, Amer. Math. Soc., 171 (1972), 195–234 | MR

[15] S. Kerov, A. Vershik, “The Grothendieck group of the infinite symmetric group and symmetric functions with the elements of the $K_0$-functor theory of {AF}-algebras”, Representation of Lie groups and related topics, Adv. Stud. Contemp. Math., 7, Gordon and Breach, 1990, 36–114 | MR

[16] R. P. Boyer, “Characters of the infinite symplectic group—a Riesz ring approach”, J. Funct. Anal., 70:2 (1987), 357–387 | DOI | MR

[17] A. M. Vershik, P. P. Nikitin, “Description of the characters and factor representations of the infinite symmetric inverse semigroup”, Funkt. Anal. Appl., 45:1 (2011), 16–30 | DOI | MR

[18] A. Okounkov, A. Vershik, “A new approach to representation theory of symmetric groups”, Selecta Math. (N.S.), 2:4 (1996), 581–605 | DOI | MR

[19] E. Thoma, “Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe”, Math. Z., 85 (1964), 40–61 | DOI | MR

[20] S. V. Kerov, Asymptotic representation theory of the symmetric group and its applications in analysis, Amer. Math. Soc., Providence, RI, 2003 | MR

[21] S. V. Kerov, A. M. Vershik, “Asymptotic theory of the characters of a symmetric group”, Funktsional. Anal. i Prilozhen., 15:4 (1981), 15–27, 96 | MR

[22] N. A. Safonkin, “Semifinite harmonic functions on the zigzag graph”, Funktsional. Anal. i Prilozhen., 56:3 (2022), 52–74 | DOI | MR

[23] T. Halverson, “Representations of the $q$-rook monoid”, J. Algebra, 273:1 (2004), 227–251 | DOI | MR