Visualizing Lie Subalgebras using Root and Weight Diagrams
Aaron Wangberg
Department of Mathematics Winona State University University Winona, MN 55987
awangberg@winona.edu
Tevian Dray
Department of Mathematics Oregon State University Corvallis, OR 97331
tevian@math.oregonstate.edu
Abstract
While Dynkin diagrams are useful for classifying Lie algebras, it is the root
and weight diagrams that are most often used in applications, such as when
describing the properties of fundamental particles. This paper illustrates
how to construct root and weight diagrams from Dynkin diagrams, and how the
root and weight diagrams can be used to identify subalgebras. In particular,
we show how this can be done for some algebras whose root and weight diagrams
have dimension greater than $3$, including the exceptional Lie algebras $F_4$
and $E_6$.