Job description / Role
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:
- the representation theory of algebraic groups,
- the theory of non-associative algebras (as concrete examples: octonion algebra, Albert algebra),
- the invariant theory of algebraic groups.
At least one article that meets the invariant theory of algebraic groups.
About the Company
Founded in 1976 by the late Sheikh Zayed Bin Sultan Al Nahyan, UAEU is a comprehensive, research-intensive university enrolling about 14,000 Emirati and international students. As the UAE’s flagship university, UAEU offers a full range of accredited, high-quality graduate and undergraduate programs through nine Colleges: Business and Economics; Education; Engineering; Food and Agriculture; Humanities and Social Sciences; IT; Law; Medicine and Health Sciences; and Science. With a distinguished international faculty, state-of-the art new campus, and full range of student support services, UAEU offers a living-learning environment that is unmatched in the UAE.
As a research-intensive university of international stature, UAEU works with its partners in industry to provide research solutions to challenges faced by the nation, the region, and the world. The University has established research centers of strategic importance to the country and the region which are advancing knowledge in critical areas ranging from water resources to cancer treatments. UAEU is currently ranked the number one research university in the GCC, number two in the Arab World, and #370 globally.
UAEU’s academic programs have been developed in partnership with employers, so our graduates are in high demand. UAEU alumni hold key positions in industry, commerce, and government throughout the region. Our continuing investments in facilities, services, and staff ensure that UAEU will continue to serve as a model of innovation and excellence.