ON REPRESENTATIONS OF ALGEBRAIC GROUPS IN CHARACTERISTIC TWO

INTRODUCTION

In this paper we investigate representations of simple algebraic groups over an algebraically closed field of characteristic 2 and of their Lie algebras. For the groups of rank 4 or less, we shall determine all of the extensions of simple modules. The central theme will be the study of some intimate connections among the groups of types B_l, C _l and D_l (and F ₄ when l = 4). We also give calculations for those other groups of rank 4 or less which have not already been treated elsewhere ([1], [18]), but this is primarily for the sake of completeness.