The Action of Generalised Symmetric Groups on Symmetric and Exterior Powers of Their Natural Representations

2015/05/31 by Bill O'Donovan, O'Donovan, Bill
Engineering · Mathematics · #20C30 #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems #math.GR #math.RT #msc:20C30

paper · pdf · doi:10.48550/arxiv.1506.00184

11 pages

arxiv created 2015/05/31 · openalex publication_date 2015/05/31 · arxiv updated 2015/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We establish upper and lower bounds on the dimension of the space spanned by the symmetric powers of the natural character of generalised symmetric groups. We adapt the methods of Savitt and Stanley from their paper `A note on the symmetric powers of the standard representation of S_n' (The Electronic Journal of Combinatorics 7 (2000), R6) to obtain bounds both over the complex numbers and in prime characteristic.

Related

• A Note on the Symmetric Powers of the Standard Representation of S_n
• The conjugacy action of S_n and modules induced from centralisers
• A formula for the base size of the symmetric group in its action on subsets
• The base size of the symmetric group acting on subsets
• A natural representation model for symmetric groups