Branching Rules and Tensor Product Decompositions in Algebraic Lie Theory

9801442 Brundan该奖项支持对一般线性群和对称群的模表示的各种分支规则的研究和计算。特别是，首席研究员感兴趣的是确定这些经典分支系数在多大程度上等于这些问题的量子版本中的类似系数。他希望既能扩展现有的基于降低算子的技术，又能利用新理解的分支规则和张量积分解之间的联系。一个并行方案是将一般线性群的完全可分表示的现有结果推广到正交群和辛群。研究支持了各种代数对象的表示理论，包括一般线性群和对称群。表征理论是确定这些对象结构的重要方法。这项工作对许多数学领域都有影响，包括环理论、群论、拓扑学和李代数的研究。

9801442 Brundan This award supports research on the study and computation of various branching rules for modular representations of general linear groups and symmetric groups. In particular, the principal investigator is interested in determining to what extent such classical branching coefficients are equal to the analogous coefficients in the quantum versions of these problems. He hopes both to extend existing techniques based on lowering operators, and to exploit newly understood connections between branching rules and decompositions of tensor products. A parallel project is to generalize existing results on completely splittable representations for general linear groups to orthogonal and symplectic groups. The research supported concerns the representation theory of various algebraic objects including general linear groups and symmetric groups. Representation theory is an important method for determining the structure of these objects. This work has implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.