A non-Levi branching rule in terms of Littelmann paths. (English) Zbl 1436.22003
Summary: We prove a conjecture of Naito-Sagaki about a branching rule for the restriction of irreducible representations of \(\mathfrak{sl}(2n,\mathbb{C})\) to \(\mathfrak{sp}(2n,\mathbb{C})\). The conjecture is in terms of certain Littelmann paths, with the embedding given by the folding of the type \(A_{2n-1}\) Dynkin diagram. So far, the only known non-Levi branching rules in terms of Littelmann paths are the diagonal embeddings of Lie algebras in their product yielding the tensor product multiplicities.
MSC:
| 22E25 | Nilpotent and solvable Lie groups |
| 05E05 | Symmetric functions and generalizations |
| 05E10 | Combinatorial aspects of representation theory |
| 20G05 | Representation theory for linear algebraic groups |
| 22E55 | Representations of Lie and linear algebraic groups over global fields and adèle rings |
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