Feb 3,8
Representations of tori. Weights. Weight multiplicity diagrams.
The Lie algebras of GL(n), SL(n), U(n), SU(n).
Weyl's unitary trick for those groups. Corollary: complete reducibility.
Thm: the irreps of SL(2) are exactly the Sym^k(C^2).
Dominance order on Z^n.
(Nonstandard) Definition: a representation V of U(n) is pointed at lambda if lambda is a weight of V, its multiplicity is 1, and lambda dominates all the other weights of V.
The Lie algebras of GL(n), SL(n), U(n), SU(n).
Weyl's unitary trick for those groups. Corollary: complete reducibility.
Thm: the irreps of SL(2) are exactly the Sym^k(C^2).
Dominance order on Z^n.
(Nonstandard) Definition: a representation V of U(n) is pointed at lambda if lambda is a weight of V, its multiplicity is 1, and lambda dominates all the other weights of V.
posted by Allen Knutson @ 7:36 PM
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