Spectral analysis and representations]Spectral analysis near regular point of reducibility and representations of Coxeter groups
Abstract
For a tuple of square matrices A1,...,An the determinantal hypersurface is defined as eqnarray* &σ(A1,...,An)= \\ &\[x1:·s :xn]∈ Pn-1: det(x1A1+·s +xnAn)=0 \. eqnarray* 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
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