Character factorizations for representations of GL(n,C)

2022/10/07 by Karmakar, Chayan
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2210.03544

Abstract

The aim of this paper is to give another proof of a theorem of D.Prasad, which calculates the character of an irreducible representation of GL(mn,ℂ) at the diagonal elements of the form \underlinet ⋅ c_n, where \underlinet=(t₁,t₂,⋯,t_m) ∈ (ℂ^*)^m and c_n=(1,ω_n,ω_n²,⋯,ω_n^n-1), where ω_n=e^{(2π\imath)/(n)}, and expresses it as a product of certain characters for GL(m,ℂ) at \underlinetⁿ.

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