We prove a conjecture of Naito–Sagaki about a branching rule for the restriction of irreducible representations of sl(2n,C) to sp(2n,C). The conjecture is in terms of certain Littelmann paths, with the embedding given by the folding of the type A2n−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.
We present a result on the number of decoupled molecules for systems binding two different types of ligands. In the case of
n
and 2 binding sites respectively, we show that there are
decoupled molecules to a generic binding polynomial. For molecules with more binding sites for the second ligand, we provide computational results.
We explicitly realize an internal action of the symplectic cactus group, originally defined by Halacheva for any finite dimensional complex reductive Lie algebra, on crystals of Kashiwara-Nakashima tableaux. Our methods include a symplectic version of jeu de taquin due to Sheats and Lecouvey, symplectic reversal, and virtualization due to Baker. As an application, we define and study a symplectic version of the Berenstein-Kirillov group and show that it is a quotient of the symplectic cactus group.
We observe that word reading is a crystal morphism. This leads us to prove that for SLn(C) the map from all galleries to Mikovic-Vilonen cycles is a surjective morphism of crystals. We also compute the fibers of this map in terms of the Littelmann path model.
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