ABSTRACT
The functions on O(:J 1) of the form g ~ (({- 1ag, 13) with a, 13 E ;!! have for derivati\·cs at g0 functions of the form x ~ (l£{1) 1ag0 , x], l3). On the other hand, the same functions arc constant on each double coset, which is a submanifold of codimension (n - I )2 • For paths in .N0 , g(O) is in u~ O(:J) and, in this condition, the derivatives generate also a (n - 1) 2 ( = n2 - I - 2(n - !))-dimensional subspace, and the proposition is proved.
