Algorithms in Linear Algebraic Groups

Abstract

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.2010 Mathematics Subject Classification. Primary 11E57, 15A21; Secondary 20G05, 15A66.