Symmetric group characters of almost square shape
Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 771-784.

We give closed product formulas for the irreducible characters of the symmetric groups related to rectangular ‘almost square’ Young diagrams p×(p+δ) for a fixed value of an integer δ and an arbitrary integer p.

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DOI: 10.5802/alco.247
Classification: 20C30, 05A15
Keywords: Characters of the symmetric groups, rectangular Young diagrams, Stanley polynomials

Matsumoto, Sho 1; Śniady, Piotr 2

1 Graduate School of Science and Engineering Kagoshima University 1-21-35 Korimoto Kagoshima Japan
2 Institute of Mathematics Polish Academy of Sciences ul. Śniadeckich 8 00-656 Warszawa Poland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Matsumoto, Sho; Śniady, Piotr. Symmetric group characters of almost square shape. Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 771-784. doi : 10.5802/alco.247. https://alco.centre-mersenne.org/articles/10.5802/alco.247/

[1] Alon, N.; Tarsi, M. Colorings and orientations of graphs, Combinatorica, Volume 12 (1992) no. 2, pp. 125-134 | DOI | MR | Zbl

[2] Biane, Philippe Representations of symmetric groups and free probability, Adv. Math., Volume 138 (1998) no. 1, pp. 126-181 | DOI | MR | Zbl

[3] Biane, Philippe Characters of symmetric groups and free cumulants, Asymptotic combinatorics with applications to mathematical physics (St. Petersburg, 2001) (Lecture Notes in Math.), Volume 1815, Springer, Berlin, 2003, pp. 185-200 | DOI | MR | Zbl

[4] De Stavola, Dario Asymptotic results for Representation Theory, Ph. D. Thesis, Universität Zürich (2017) (Preprint arXiv:1805.04065v1)

[5] Ivanov, V.; Kerov, S. The algebra of conjugacy classes in symmetric groups, and partial permutations, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), Volume 256 (1999), p. 95-120, 265 | DOI | MR | Zbl

[6] Matsumoto, Sho; Śniady, Piotr Linear versus spin: representation theory of the symmetric groups, Algebr. Comb., Volume 3 (2020) no. 1, pp. 249-280 | DOI | MR | Zbl

[7] Mingo, James A.; Speicher, Roland Free probability and random matrices, Fields Institute Monographs, 35, Springer, New York; Fields Institute for Research in Mathematical Sciences, Toronto, ON, 2017, xiv+336 pages | DOI | MR

[8] Sagan, Bruce E. The symmetric group. Representations, combinatorial algorithms, and symmetric functions., Grad. Texts Math., 203, New York, NY: Springer, 2001 | Zbl

[9] Schur, J. Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, J. Reine Angew. Math., Volume 139 (1911), pp. 155-250 | DOI | MR | Zbl

[10] Stanley, Richard P. Irreducible symmetric group characters of rectangular shape, Sém. Lothar. Combin., Volume 50 (2003/04), p. Art. B50d, 11 pages | MR | Zbl

[11] Stanley, Richard P. Enumerative combinatorics. Volume 1, Cambridge Studies in Advanced Mathematics, 49, Cambridge University Press, Cambridge, 2012, xiv+626 pages | MR

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