Finite reflection groups and related topics

Faculty Member

Shiang Tang

Finite reflection groups arise from the study of symmetries of regular polytopes. For example, the symmetry group of regular tetrahedron is isomorphic to the permutation group of {1,2,3,4}.
An important class of finite reflection groups is the Weyl groups, which arise from the theory of Lie algebras. They are symmetry groups of certain configurations in vector spaces over R (called root systems).

Jacques Tits defined and studied the extended Weyl groups, which are variants of the Weyl groups. In this project, we will study specific examples of extended Weyl groups: orders of their elements, subgroups. We will also look for explicit rational polynomials whose Galois groups are isomorphic to certain Weyl groups.

Team Meetings

weeky

Project Difficulty

Intermediate

Undergrad Prerequisites

Math 416 and Math 417 are required.