Branching Laws Aim Lectures July
نویسندگان
چکیده
A basic problem in the representation theory of a compact Lie group is to calculate the restriction of an irreducible representation of K to a closed subgroup. Most classical results on this problem concern connected groups. We’ll recall some of those, and talk about some of the modifications needed to work with disconnected groups. 1. Weight multiplicities Suppose g is a complex semisimple Lie algebra and h a Cartan subalgebra. If we fix a Borel subalgebra b = h + n of g, then the irreducible finite-dimensional representations of g are parametrized by dominant integral weights h. Write V λ for the representation of highest weight λ. The restriction of V λ to h is a direct sum of weight spaces: V |h = ⊕
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