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Rational representations of some algebraic varieties of \(M\)-orthogonal groups. (English) Zbl 0953.20039

Let \(M\) be an \(n\times n\)-matrix with real coefficients. The group \(\{A\in\text{GL}(n,\mathbb{R})\mid AMA^\top=M\}\) is called \(M\)-orthogonal group. Rational parametrizations of \(M\)-orthogonal groups and some of their subgroups are given in this paper.

MSC:

20G20 Linear algebraic groups over the reals, the complexes, the quaternions
20G05 Representation theory for linear algebraic groups
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