English
Define genWeightSpaceChain as the supremum of genWeightSpace over all k between p and q: genWeightSpaceChain M χ1 χ2 p q = ⨆ k ∈ Ioo p q, genWeightSpace M (k • χ1 + χ2).
Русский
Определим chainWeighted как супремум весовых пространств для всех k между p и q: genWeightSpaceChain M χ1 χ2 p q = ⨆ k ∈ Ioo p q, genWeightSpace M (k • χ1 + χ2).
LaTeX
$$$\text{genWeightSpaceChain}(M, \chi_1, \chi_2, p, q) = \big\luggage_{k \in Ioo(p,q)} genWeightSpace(M, k \cdot χ_1 + χ_2)\big\rbrace$$$
Lean4
/-- Given two (potential) weights `χ₁` and `χ₂` together with integers `p` and `q`, it is often
useful to study the sum of weight spaces associated to the family of weights `k • χ₁ + χ₂` for
`p < k < q`. -/
def genWeightSpaceChain : LieSubmodule R L M :=
⨆ k ∈ Ioo p q, genWeightSpace M (k • χ₁ + χ₂)
