Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula

dc.creatorRattan, Amarpreet
dc.creatorSniady, Piotr
dc.date2006-10-18
dc.date2007-03-21
dc.date.accessioned2026-07-07T09:32:05Z
dc.date.available2026-07-07T09:32:05Z
dc.descriptionWe study asymptotics of an irreducible representation of the symmetric group S_n corresponding to a balanced Young diagram λ(a Young diagram with at most C\sqrt{n} rows and columns for some fixed constant C) in the limit as n tends to infinity. We show that there exists a constant D (which depends only on C) with a property that |χ^λ(π)| = | Tr ρ^λ(π)/Tr ρ^λ(e) | < [ D max(1,|π|^2/n) / \sqrt{n}} ]^{|π|}, where |π| denotes the length of a permutation (the minimal number of factors necessary to write πas a product of transpositions). Our main tool is an analogue of Frobenius character formula which holds true not only for cycles but for arbitrary permutations.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0610540
dc.identifierhttp://arxiv.org/abs/math/0610540
dc.identifierAdvances in Mathematics 218 (2008) 673-695
dc.identifierdoi:10.1016/j.aim.2008.01.008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158685
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject20C30; 05E10; 46L54
dc.titleUpper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula
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