On multiplicities of maximal weights of sl(n)-modules

2013/09/19 by Rebecca L. Jayne, Kailash C. Misra, Jayne, Rebecca L. +1
Mathematics · #17B65 #17B67 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B65 #msc:17B67

paper · pdf · doi:10.48550/arxiv.1309.4969

17 pages

arxiv created 2013/09/19 · arxiv updated 2013/09/20

Abstract

We determine explicitly the maximal dominant weights for the integrable highest weight sl(n)-modules V((k-1)Λ₀ + Λ_s), 0 ≤ s ≤ n-1, k ≥ 2. We give a conjecture for the number of maximal dominant weights of V(kΛ₀) and prove it in some low rank cases. We give an explicit formula in terms of lattice paths for the multiplicities of a family of maximal dominant weights of V(kΛ₀). We conjecture that these multiplicities are equal to the number of certain pattern avoiding permutations. We prove that the conjecture holds for k=2 and give computational evidence for the validity of this conjecture for k >2.

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