## 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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