This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double coset decomposition with respect to a Siegel maximal parabolic subgroup, which is important in computing infinite-dimensional representations for some algebraic groups.

中文翻译：

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线性代数群中的算法

本文介绍了线性代数群中的一些算法。这些算法解决了单词问题并计算正交群的旋量范数。这为我们提供了旋量范数的算法定义。我们计算关于 Siegel 最大抛物线子群的双陪集分解，这对于计算某些代数群的无限维表示很重要。