Fix for SUNRepresentations type parameter change (#426)

* Fix for SUNRepresentations type parameter change

* Use `SUNRepresentations.casimir`, bump compat to 0.4

* Remove rogue backticks

Author: leburgel

docs/Project.toml

@@ -16,6 +16,6 @@ TensorKit = {path = ".."}
 [compat]
 Documenter = "1"
 DocumenterInterLinks = "1"
-SUNRepresentations = "0.3"
+SUNRepresentations = "0.4"
 Test = "1"
 WignerSymbols = "1,2"

docs/src/appendix/symmetric_tutorial.md

@@ -959,22 +959,16 @@ The eigenvalue of the quadratic Casimir for a given irrep is given by [Freudenth
 ```math
 \Omega(D(p,q)) = \frac{1}{3} (p^2 + q^2 + 3p + 3q + pq).
 ```
-Using SUNRepresentations.jl, we can compute the Casimir as
-```@example symmetric_tutorial
-function casimir(l::SU3Irrep)
-    p, q = dynkin_label(l)
-    return (p^2 + q^2 + 3 * p + 3 * q + p * q) / 3
-end
-```
+This can be computed using SUNRepresentations.jl's `casimir` method, where `casimir(2, l)` returns the quadratic Casimir for irrep `l`.
 If we use the adjoint representation of ``\mathsf{SU}_3`` as physical space, the Heisenberg exchange interaction can then be constructed as
 ```@example symmetric_tutorial
-V = Vect[SUNIrrep{3}](SU3Irrep("8") => 1)
+V = Vect[SU3Irrep](SU3Irrep("8") => 1)
 TT = zeros(ComplexF64, V ⊗ V ← V ⊗ V)
 for (s, f) in fusiontrees(TT)
     l3 = f.uncoupled[1]
     l4 = f.uncoupled[2]
     k = f.coupled
-    TT[s, f] .= (casimir(k) - casimir(l3) - casimir(l4)) / 2
+    TT[s, f] .= (casimir(2, k) - casimir(2, l3) - casimir(2, l4)) / 2
 end
 subblocks(TT)
 ```