Good question. I've found this to be a difficult subject to get into myself. An abstract approach can seem arcane, but concrete constructions can be complicated and messy. You might try the paper by Hersh and Lenart as a starting point. They take a concrete approach, which has the advantage that you can start computing with small examples relatively quickly. A disadvantage is that your student might miss the big picture of how all this fits into the general representation theory of classical Lie algebras. For that, perhaps the work of Molev, such as this paper, might be helpful.

Good question. I've found this to be a difficult subject to get into myself. An abstract approach can seem arcane, but concrete constructions can be complicated and messy. You might try the paper Hersh and Lenart - Combinatorial construction of weight bases: The Gelfand–Tsetlin basis as a starting point. They take a concrete approach, which has the advantage that you can start computing with small examples relatively quickly. A disadvantage is that your student might miss the big picture of how all this fits into the general representation theory of classical Lie algebras. For that, perhaps the work of Molev, such as Molev - Gelfand–Tsetlin bases for classical Lie algebras, might be helpful.