UNICITY OF A1-SUBGROUPS ASSOCIATED TO UNIPOTENT ELEMENTS IN SIMPLE ALGEBRAIC GROUPS

Let k be an algebraically closed field of positive characteristic and G a simple algebraic group over k. Under the assumption that the characteristic is a good prime for G, we determine which unipotent elements u ∈ G, with u of order p, satisfy the property that any two A1-subgroups of G containing u are G-conjugate. This result establishes to what degree an analog of the theorems of Jacobson-Morozov and Kostant for Lie algebras are valid for simple algebraic groups defined over fields of (good) positive characteristic.