isomorphismOfRepresentations -- compute an explicit isomorphism between two Lie algebra representations

Let $\rho_1: \mathfrak{g} \rightarrow \mathfrak{gl}(V_1)$ and $\rho_2: \mathfrak{g} \rightarrow \mathfrak{gl}(V_2)$ be two representations, and suppose that $\rho_1 \cong \rho_2$. Then this function returns matrix $P$ such that $\rho_2(X) = P^{-1}*rho_1(X)*P$ for each $X \in \mathfrak{g}$.

To find $P$, we first express the basis of $V_2$ as words in the lowering operators using basisWordsFromMatrixGenerators. We then evaluate these words using the matrix generators for $\rho_1$ to construct the matrix $P$.

In the example below, we compute an isomorphism between the adjoint representation of $sl_3$ (built using the textbook basis of $sl_3$) and the Gelfand-Tsetlin basis for the adjoint representation of $sl_3$.

We check that the matrix $P$ has the property that $\rho_2(X) = P^{-1}*rho_1(X)*P$ for each $X \in \mathfrak{g}$. (The function isomorphismOfRepresentations performs this check automatically before returning the matrix $P$.)