Gelfand--Tsetlin pattern and strict partitions (Q1402293)

To any partition \(\lambda\) of length less than or equal to an integer \(m\), it is associated an irreducible polynomial representation \(V_m^{\lambda}\) of \(\text{GL}(m)\). Restricting the action to \(\text{GL}(m-1)\) we get a decomposition of \(V_m^{\lambda}\). An irreducible \(V_{m-1}^{\mu}\) for \(\text{GL}(m-1)\) appears in this decomposition (with multiplicity one) if and only if \(\lambda_{i+1}\leq \mu_i \leq \lambda_i\) for \(i=1,\ldots, m-1\). Repeating this for \(m-2, m-3, \ldots \) we get a sequence of partitions, called a Gelfand-Tsetlin pattern. On the other hand, it is known that highest weights for irreducible tensor representations of the queer Lie superalgebra are parametrized by strict partitions. The paper shows that a Gelfand-Tsetlin pattern with strict partitions may be viewed as consecutive branching rules for the queer Lie superalgebra.