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Series of Lie groups

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MA469 Fourth Year Research Project.
Lieven Le Bruyn has been blogging about representations of subgroups
of the modular group. Here are the relevant pages listed in the order
in which they
were posted. These groups are important and geometrical. The representations
of these groups are studied using path algebras.
Hexagonal Moonshine
The Dedekind tessellation
Modular quilts and cuboid tree diagrams
Hyperbolic Mathieu polygons
Farey codes
Hexagonal moonshine
Generators of modular groups
Hexagonal Moonshine
There are (at least) two possible projects. One project would be based
on the geometry and group theory. The idea would be to take the ideas
which have been presented in these posting in an informal style and to
present them in a more coherent and scholarly style. The other project
is more ambitious. Lieven is an expert on the representation theory
and so he does not discuss his approach here as he already understands it.
The project would then give the statements of some general results and
then show how they applied in these examples.
This is a project for Fourth Year MMath students.
Series of Lie groups
The focus of my research is on the idea of series of Lie groups.
Here are the
slides
from a talk.