Anthony Joseph
The Donald Frey Professor
My field of research is algebra and
more particularly representation theory. Briefly, representation theory provides
a grand unification of the relations of classical functions which themselves
enter into almost every scientific arena. In the last two decades more complex
algebraic relations have been unraveled from conformal field theory and statistical
physics. Deep new methods have spun out solutions to these extraordinarily intricate
equations. Of particular interest is the theory of "crystals" which derive from
quantum groups. These developments will be of fundamental importance to the
mathematics and physics of the twenty-first century. Our group had previously
been a part of a European TMR network "Algebraic Lie Representations". It is
now part of the European RTN network, "Liegrits" whose activities will shortly
begin.
Recent Publications
- A decomposition theorem for Demazure crystals. J. Algebra 265 (2003) 562-578.
- On the graded injectivity of the Conze embedding. J. Algebra 265 (2003) 358-378.