Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula
| dc.creator | Rattan, Amarpreet | |
| dc.creator | Sniady, Piotr | |
| dc.date | 2006-10-18 | |
| dc.date | 2007-03-21 | |
| dc.date.accessioned | 2026-07-07T09:32:05Z | |
| dc.date.available | 2026-07-07T09:32:05Z | |
| dc.description | We 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.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610540 | |
| dc.identifier | http://arxiv.org/abs/math/0610540 | |
| dc.identifier | Advances in Mathematics 218 (2008) 673-695 | |
| dc.identifier | doi:10.1016/j.aim.2008.01.008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158685 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20C30; 05E10; 46L54 | |
| dc.title | Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula | |
| dc.type | text |