**REU Homepage of Christopher
Sadowski**

**(Root
system of G_2)**

## Representation Theory of Affine Lie Algebras and Vertex
Operator
Algebras

Advisors: William Cook and Yi-Zhi Huang

My email: csadowski [at] gmail [dot] com

For a quick rundown of the things this project deals with
(basic
definitions, ideas, etc.), click here: Notes
and
Definitions

For an example of an affine Lie algebra module which has
vertex operator
algebra structure, click here: A
semi-construction

REU Final Presentations: For my slideshow presentation along
with some results, click here: Slides
and Results

Slides from my talk at the GSUMC: Slides

Announcements:

April
2008: I will be speaking about my project and results on
Saturday, April 12, 2008
at the Garden State Undergraduate Math Conference. Slides
will be
posted shortly, or come to the conference to see them presented :).

March
2008: After a Fall semester hiatus, we've resumed work on the
project. Details and paper to come.

Update(8/22/07): We have found patterns and have results for
all simple Lie algebras! We now know the behavior
for ALL
simple Lie algebras, a huge step up from the results in the slides
above. Bill Cook has written a Maple program
that has verified that our patterns hold. Only proofs remain.

August
2007: Types A_1, A_2, A_3, A_4, D_4, E_8, F_4, G_2 have been worked
out, and things seem messy. See the REU Final Presentations
slides posted above for more

information.

Links:

My Rutgers Math Homepage

Gmail

Last Update: 06/20/08

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