This is to continue my previous project on vector invariants and separating vector invariants of exceptional simple groups over infinite fields of positive characteristic. The main targets of the investigation are the invariants of the groups G_2 and F_4. During the last RA's visit we developed some approach to the most difficult case : vector (separating) invariants of G_2 over a field of characteristic 2 (the case of odd characteristic is completely described in my article with prof. I.Shestakov). Using the triality principle in the projective special orthogonal group PSGO(8), we reduced this problem to the problem of orbit separating for a certain action of the group SO(7) on the space of several copies of octonions and one copy of the induced SO(7)-module of highest weight omega_1+omega_2+omega_3. I suspect that during the second RA's visit we will completely describe multilinear invariants and check whether they separate orbits in the above mentioned representation of SO(7).
The candidate should have a decent background in : 1) the representation theory of algebraic groups, 2) the theory of non-associative algebras (as concrete examples : octonion algebra, Albert algebra), 3) the invariant theory of algebraic groups.
At least one article that meets the invariant theory of algebraic groups.
Special Instructions to Applicant
Division College of Science - (COS)
Department Mathematical Sciences - (COS)
Job Close Date 31-12-2021
Job Category Academic - Research Assistant