Spectral Analysis Near Regular Point of Reducibility and Representations of Coxeter Groups

Michael I. Stessin ()
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Michael I. Stessin: University at Albany, Department of Mathematics and Statistics

A chapter in Multivariable Operator Theory, 2023, pp 769-798 from Springer

Abstract: Abstract For a tuple of square matrices $$A_1,\ldots ,A_n$$ A 1 , … , A n the determinantal hypersurface is defined as $$\begin{aligned}&\sigma (A_1,...,A_n) \\&\quad =\Big \{[x_1:\cdots :x_n]\in {{\mathbb {C}}}{{\mathbb {P}}}^{n-1}: det(x_1A_1+\cdots +x_nA_n)=0\Big \}. \end{aligned}$$ σ ( A 1 , . . . , A n ) = { [ x 1 : ⋯ : x n ] ∈ C P n - 1 : d e t ( x 1 A 1 + ⋯ + x n A 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.

Keywords: Projective joint spectrum; Detarminantal manifold; Coxeter groups; Representations of coxeter groups; Primary 47A25; 47A13; 47A75; 47A15; 14J70; Secondary 47A56; 47A67 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-50535-5_28

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DOI: 10.1007/978-3-031-50535-5_28

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