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Questions about the branch of algebra that deals with groups.
2
votes
Kostant partition function: asymptotics and specifics
To expand on Jim's answer, it's a result of Kostant that for any weight $\mu$ and any dominant weight $\lambda$ the dimension of the $\mu$-weight space of the induced module $H^0(\lambda)$ with highes …
4
votes
subgroups with the same number of roots that the group.
A good modern introduction to the subject is given in Martin Liebeck's survey article "Introduction to the subgroup structure of algebraic groups." It's a chapter in the book "Representations of Reduc …