 This makes sense of numerous phenomena, such as 'lifting' of forms from one group to another larger one, and the general fact that certain groups that become isomorphic after field extensions have related automorphic representations.From a reductive algebraic group over a separably closed field "K" we can construct its root datum ("X"*, Δ,"X"*, Δv), where 
"X"* is the lattice of characters of a maximal torus, "X"* the dual lattice (given by the 1-parameter subgroups), Δ the roots, and Δv the coroots.A connected reductive algebraic group over "K" is uniquely determined (up to isomorphism) by its root datum.