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

### Authors:

- Amarpreet Rattan,
- Piotr Śniady

### Abstract

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) | = | frac(Tr ρ^{λ} (π), Tr ρ^{λ} (e)) | ≤ (frac(D max (1, frac(| π |^{2}, n)), sqrt(n)))^{| π |}, where | π | denotes the length of a permutation (the minimal number of factors necessary to write π as a product of transpositions). Our main tool is an analogue of the Frobenius character formula which holds true not only for cycles but for arbitrary permutations. © 2008 Elsevier Inc. All rights reserved.

- Record ID
- UAM160219dfdb3a447a92765a0635e2e4e1
- Author
- Journal series
- Advances in Mathematics, ISSN 0001-8708
- Issue year
- 2008
- Vol
- 218
- Pages
- 673-695
- ASJC Classification
- DOI
- DOI:10.1016/j.aim.2008.01.008 opening in a new tab
- Language
- en English
- Score (nominal)
- 45
- Score source
- journalList
- Publication indicators
- = 9.000; : 2008 = 1.933; : 2008 = 1.280 (2) - 2008=1.429 (5)

- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAM160219dfdb3a447a92765a0635e2e4e1/

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perishopening in a new tab system.

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