Investigate slow Littlewood–Richardson tensor products in type A for large rank

[pbelmans]

In type A, Semisimple.jl has two algorithms for computing tensor products: Brauer–Klimyk and one based on Littlewood–Richardson coefficients. The LR-based approach is the default because it is vastly faster in small cases.

In type $\mathrm{A}_7$, however, computing $\mathrm{V}(\rho)\otimes\mathrm{V}(\rho)$ shows the default is already much slower than Brauer–Klimyk:

using Semisimple
ρ = weyl_vector(TypeA{7})

@time tensor_product(ρ, ρ)                                          # 35.18 s
@time Semisimple._brauer_klimyk_dominant(dominant_character(ρ), ρ)  # 0.07 s

Both return the same character. This came up while verifying Kostant's conjecture.

Two things to look into:

1. Is there an improvement to be made in the LR implementation, so it remains competitive at higher rank?
2. If not, expose an option to choose the algorithm in type A (or switch the default above some threshold).