Fundamental weights, permutation weights and 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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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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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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If prices of individual stocks are unbiased but noisy approximations to fundamental values, there will be a gap in returns between the standard cap-weighted market portfolio and the one based on fundamentals. The discrepancy occurs because, relative to fundamentals, cap-weights are too large (small) for stocks with positive (negative) deviations from fundamental values. It follows that the usua...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1999
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/32/9/016