On a conjecture by Naito-Sagaki: Littelmann paths and Littlewood-Richardson Sundaram tableaux

2016/05/23 by Jacinta Torres, Torres, Jacinta
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1605.07135

13 pages. Comments welcome

arxiv created 2016/05/23 · arxiv updated 2017/08/07

Abstract

We prove a special case of a conjecture of Naito-Sagaki about a branching rule for the restriction of irreducible representations of \mathfraksl(2n,ℂ) to \mathfraksp(2n,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. We propose and motivate an approach to the conjecture in general, in terms of Littlewood-Richardson Sundaram tableaux.

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