Linear versus spin: representation theory of the symmetric groups
Algebraic Combinatorics, Volume 3 (2020) no. 1, pp. 249-280.

We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition ξ with analogous normalized linear characters evaluated on the double partition D(ξ). We also relate some natural filtration on the usual (linear) Kerov–Olshanski algebra of polynomial functions on the set of Young diagrams with its spin counterpart. Finally, we give a spin counterpart to Stanley formula for the characters of the symmetric groups in terms of counting maps.

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DOI: 10.5802/alco.92
Classification: 20C25,  20C30,  05E05
Keywords: Projective representations of the symmetric groups, linear representations of the symmetric groups, asymptotic representation theory, Stanley character formula
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 00-956 Warszawa Poland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Matsumoto, Sho; Śniady, Piotr. Linear versus spin: representation theory of the symmetric groups. Algebraic Combinatorics, Volume 3 (2020) no. 1, pp. 249-280. doi : 10.5802/alco.92. https://alco.centre-mersenne.org/articles/10.5802/alco.92/

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