Osaka Journal of Mathematics

On the classifications of unitary matrices

Krishnendu Gongopadhyay, John R. Parker, and Shiv Parsad

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We classify the dynamical action of matrices in $\mathrm{SU}(p, q)$ using the coefficients of their characteristic polynomial. This generalises earlier work of Goldman for $\mathrm{SU}(2, 1)$ and the classical result for $\mathrm{SU}(1, 1)$, which is conjugate to $\mathrm{SL}(2, \mathbb{R})$. As geometrical applications, we show how this enables us to classify automorphisms of real and complex hyperbolic space and anti de Sitter space.

Article information

Osaka J. Math., Volume 52, Number 4 (2015), 959-993.

First available in Project Euclid: 18 November 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51F25: Orthogonal and unitary groups [See also 20H05]
Secondary: 20H20: Other matrix groups over fields


Gongopadhyay, Krishnendu; Parker, John R.; Parsad, Shiv. On the classifications of unitary matrices. Osaka J. Math. 52 (2015), no. 4, 959--993.

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