Mathematical Sciences: Lie and Nonassociative Algebras

本课题主要研究了中心化子代数、插入方案、稳定性和分次李代数的构造。主要研究人员将研究复单李代数表示的张量积，以及当正交李代数的秩渐近无穷时，旋量表示的行为。此外，她还将研究分次李代数的构造，以此为手段系统地探索具有小特征的单李代数，并确定Gim和Kac-Moody代数的根的重数。这个项目是关于物理学、组合学、代数几何和特征p代数的接口。它涉及自韦尔和布劳尔时代以来悬而未决的建设性代表性问题。这些问题目前引起了组合学家和物理学家的极大兴趣。

This project is concerned with centralizer algebras, insertion schemes, stability and constructions of graded Lie algebras. The principal investigator will study tensor products of representations of complex simple Lie algebras and the behavior of spinor representations as the rank of the orthogonal Lie algebra goes to infinity. In addition, she will study constructions of graded Lie algebras as a means of systematically exploring simple Lie algebras of small characteristic and of determining root multiplicities for GIM and Kac-Moody algebras. This project is on the interface of physics, combinatorics, algebraic geometry and characteristic p algebra. It involves constructive representation questions left hanging since the time of Weyl and Brauer. These questions are presently of great interest to combinatorialists and physicists.