9401389 Lin The principal investigator will study further relations between quantum groups and the representations of algebraic groups in characteristic p. The first part of the research is to study various intertwining homomorphisms over an integral domain for quantum groups. This will provide a new class of homomorphisms for Weyl modules. The second part of the research is to study the contravariant bilinear forms on a quantum Weyl module over an integral domain by using the Joseph inductions to explore the relations between the Jantzen filtrations for both quantum groups and algebraic groups. The last problem is to explore the Andersen-Jantzen-Soergel localization technique in the comparison hyperalgebras. Quantum groups are a new area of research for both mathematicians and physicists. On the mathematical side, it combines three of the oldest areas of "pure" mathematics, algebra, analysis and geometry, yet it is of great interest to physicists working on conformal quantum field theory.
