Young Tableux and representation theory

[Haelfix]

Hey guys, I was just wondering if you have a good references to the use of Young diagrams/Tableuxs specifically to deduce the representation theory of various Lie groups *other than SU(N)*

I know how it works for SU(N) and those groups that can be split into tensor copies theoreof, but I have no idea how to use them for say SO(7) (and I am pretty sure it can be done).

I know how to find the reps using root/weight systems, but Young diagrams are so much easier to use imo.

 

[Chris Hillman]

Try the book by Daniel Bump, Lie Groups, Springer, 2000, e.g. see the detailed discussion of SO(9) on p. 263.

 

[tacman]

Thank you for your question! Young tableux and representation theory are definitely powerful tools for understanding the structure of Lie groups and their representations. While they are commonly used for SU(N) groups, they can also be applied to other Lie groups such as SO(7).

One reference that I would recommend for understanding the use of Young tableux in representation theory is the book "Lie Groups, Lie Algebras, and Representations: An Elementary Introduction" by Brian C. Hall. This book provides a clear and comprehensive explanation of how to use Young tableux to deduce the representation theory of various Lie groups, including SO(7).

Another helpful resource is the paper "Young's Tableaux and the Representation Theory of the Classical Groups" by William Fulton. This paper provides a detailed analysis of the use of Young tableux in representation theory for classical Lie groups, including SO(7).

I hope these references will be useful for you in understanding how to use Young tableux for Lie groups other than SU(N). Good luck in your studies!