Spectral analysis and representations]Spectral analysis near regular point of reducibility and representations of Coxeter groups

2022/03/14 by Stessin, Michael · 2 citations
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2203.07221

Abstract

For a tuple of square matrices A₁,...,A_n the determinantal hypersurface is defined as amp;σ(A₁,...,A_n)=
amp;\[x₁:⋯ :x_n]∈ \C\mathbb P^n-1: det(x₁A₁+⋯ +x_nA_n)=0 \. In this paper we develop a local spectral analysis near a regular point of reducibility of a determinantal hypersurface. We prove a rigidity type theorem for representations of Coxeter groups as an application

Cited by

• Coxeter groups and the proper joint spectrums of their faithful representations
• Spectral test of reducibility for Matrix tuples

Related

• Projective Joint Spectra and Characters of representations of A_n
• Decomposability of local determinantal representations of hypersurfaces
• Representation Theory and Differential Equations
• Determinantal hypersurfaces
• Determinants of Representations of Coxeter Groups