Subgroups of a spinor group containing a maximal split torus. I

This paper studies subgroups of the split spinor groupG=Spin (n, k),n 6, over a field K containing a maximal split torus T=T(n,K)assuming that charK2and ||K ||7.The main result of the first pan of the paper is the reduction of the proof that subgroups containing T are standard to the study of subgroups not containing root unipotent elements.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 49–75, 1991.