Young Tableux and representation theory

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SUMMARY

The discussion focuses on the application of Young diagrams and tableaux in deducing the representation theory of Lie groups, specifically beyond SU(N). The user seeks references for using these tools with groups like SO(7). Daniel Bump's book, "Lie Groups" (Springer, 2000), is recommended for its detailed analysis of SO(9) on page 263, highlighting the effectiveness of Young diagrams compared to root/weight systems.

PREREQUISITES
  • Understanding of representation theory of Lie groups
  • Familiarity with Young diagrams and tableaux
  • Knowledge of root and weight systems
  • Basic concepts of Lie groups, particularly SO(N)
NEXT STEPS
  • Research the application of Young tableaux in representation theory for SO(7)
  • Study the detailed examples in Daniel Bump's "Lie Groups" for practical insights
  • Explore the representation theory of other Lie groups using Young diagrams
  • Learn about the relationship between root systems and Young tableaux
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, and researchers interested in advanced representation theory, particularly those focusing on Lie groups and the application of Young diagrams in their studies.

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

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