Date of Submission
Project Advisor 1
A Lie group is a group that is also a differentiable manifold, such that the group operation is continuous respect to the topological structure. To every Lie group we can associate its tangent space in the identity point as a vector space, which is its Lie algebra. Killing and Cartan completely classified simple Lie groups into seven types. Representation of a Lie group is a homomorphism from the Lie group to the automorphism group of a vector space. In general represenations of Lie group are determined by its Lie algebra and its the connected components. We may consider operations like direct sum and tensor product with respect to which the representations of G form a ring R(G). Assume the group is compact. For every Lie group we may find a maximal torus inside of it. By projecting the representation ring of the Lie group to the representation ring of its maximal torus, we may consider to express R(T) elements as sums of products of base elements with R(G) elements. In 1970s Pittie and Steinberg proved R(T) is a free module over R(G) using homological algebra methods without specifying the bases in each seven types. In this senior project I found an explicit basis for the representation ring of the maximal torus of Lie group SUn in terms of the represenation ring of the Lie group itself. I also did some computation with SO2n.
Access restricted to On-Campus only
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Zhou, Changwei, "Bases for representation rings of Lie groups and their maximal tori" (2012). Senior Projects Spring 2012. 238.
This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.Bard Off-campus Download
Bard College faculty, staff, and students can login from off-campus by clicking on the Off-campus Download button and entering their Bard username and password.