Take G to be a split, simply-connected semisimple algebraic group (for example, SL(w, K) or Sp(2m, K)) over an algebraic closure K of the field of p elements, where p is prime. Denote by G(n) the finite subgroup consisting of elements of G defined over the field of p elements. The simple (rational) G-modules L(X) are parametrized by the set X of dominant weights, a subset of the character group...

Let A be a symmetrizable generalized Cartan matrix. Let g be the corresponding Kac-Moody algebra. Let G(R) be Tits’ Kac-Moody group functor over commutative rings R associated to g. Then G(R) is given by five axioms KMG1-KMG5 which are natural extensions of the properties of Chevalley-Demazure group schemes. We give a construction of the Tits functor for symmetrizable Kac-Moody groups G using i...