On the minimal dimensions of irreducible representations of symmetric groups

1983/11/01 by Gordon James · 93 citations
Mathematics · Computer Science · #Finite Group Theory Research #Advanced Algebra and Geometry #Coding theory and cryptography #Irreducible representation #Mathematics #Symmetric group #Integer (computer science) #Degree (music) #Combinatorics #Group (periodic table) #Field (mathematics) #Pure mathematics #Computer science #Physics

paper · doi:10.1017/s0305004100000803

published in Mathematical Proceedings of the Cambridge Philosophical Society 94(3), 417-424 (Cambridge University Press)

openalex publication_date 1983/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

For each integer m , Rasala [6] has shown how to list all the ordinary irreducible representations of the symmetric group n which have degree less than n m , provided that n is large enough, and in this note we shall prove similar results for the irreducible representations of n over an arbitrary field K. Our estimates are very crude, so although we recover Rasala's results, we get nowhere near his precise information on how large n has to be.

Citations

• On the minimal degrees of characters of Sn

Cited by

• Irreducibility of the Lawrence-Krammer representation of the BMW algebra of type A_n-1, PhD thesis California Institute of Technology 2008
• Growth of cross-characteristic representations of finite quasisimple groups of Lie type
• Representation theory of the symmetric group [wikipedia]