Representation Theory: From Quantum Groups to Algebraic Groups

9401389 林 主要研究者将进一步研究量子群和代数群的表征之间的关系，在特征p.研究的第一部分是研究量子群的整数域上的各种交织同态。这将为Weyl模提供一类新的同态。 第二部分研究整环上量子Weyl模上的逆变双线性型，利用Joseph诱导讨论量子群和代数群的Jantzen滤子之间的关系。 最后一个问题是探讨比较超代数中的Andersen-Jantzen-Soergel局部化技巧。 量子群是数学家和物理学家研究的一个新领域。 在数学方面，它结合了三个最古老的领域的“纯”数学，代数，分析和几何，但它是非常感兴趣的物理学家工作的共形量子场论。

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.