Abstract
We propose a conjecture describing the branching rule, in terms of Littelmann's path model, from the special linear Lie algebra sl 2 n ( C ) (of type A 2 n − 1 ) to the symplectic Lie algebra (of type C n ) embedded as the fixed point subalgebra of the diagram automorphism of sl 2 n ( C ) . Moreover, we prove the conjecture in certain cases, and also provide some supporting examples. In addition, we show that the branching coefficients can be obtained explicitly by using the inverse Kostka matrix and path models for tensor products of symmetric powers of the defining (or natural) representation C 2 n of sl 2 n ( C ) .
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