Conditions on a compact connected Lie group which insure a ‘‘Weyl character formula”
نویسندگان
چکیده
منابع مشابه
The Weyl Character Formula
We have seen that irreducible representations of a compact Lie group G can be constructed starting from a highest weight space and applying negative roots to a highest weight vector. One crucial thing that this construction does not easily tell us is what the character of this irreducible representation will be. The character would tell us not just which weights occur in the representation, but...
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and note that 〈h, e, f〉 = sl2(C). Let u, v be the canonical basis of E = C2. Then each SymE is irreducible with ud spanning the highest-weight space of weight d and, up to isomorphism, SymE is the unique irreducible sl2(C)module with highest weight d. (See Exercises 1.1 and 1.2.) The diagram below shows the actions of h, e and f on the canonical basis of SymE: loops show the action of h, arrows...
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G is a connected reductive complex Lie group T ⊂ B is a maximal torus contained in a Borel subgroup of G g, b, t are the Lie algebra of G, B, T . R, Ř are the sets of roots and coroots of T in g, R, Ř are the roots of T in b and their coroots, φα : SL2(C)→ G the homomorphism arising from the sl2-triple (eα, hα, fα) in g (for α ∈ R). X = {λ ∈ t× : 〈λ, Ř〉 ⊂ Z}. X = {λ ∈ X : 〈λ, Ř〉 ⊂ Z≥0}. X̌ = ZŘ ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0367117-7