代数群与不变量

李理论，特别是代数群和量子群是数学研究的核心领域之一，在过去的几十年中，该领域(特别是代数群的模表示理论)有了很大的进展。著名数学家 George Lusztig, J.C.Jantzen, H.H.Andersen, Wolfgang Soergel, Peter Fiebig, Geordie Williamson 都活跃在该领域。如何刻画不变量，也是代数群表示论的基本问题之一。近年来，S.-T. Yau 等人将复流形的孤立奇点分类从某种程度上归结为复代数群表示的不变Jacobian空间问题。本项目致力于研究特征 p 域上的代数群的不变 Jacobian 空间的刻画问题。

Lie theory, especially the theory of algebraic groups and quantum groups play an important role in mathematical study and it have been made great progress in last decades. George Lusztig, J.C.Jantzen, H.H.Andersen, Wolfgang Soergel, Peter Fiebig, Geordie Williamson have made great contribution to these direction. One of the fundamental problem in representation theory of algebraic groups is to discribe the invariants. Recently, S.-T. Yau reduces the problem of classifying isolated singularities to the problem of discribe the invariant Jacobian for the action of complex algebraic group. Our project devotes to the discribe the invariant Jacobian for the action of algebraic group over field of characteristic p>0.