2022/08/15 by Rebecca L. Jayne, Kailash C. Misra, Jayne, Rebecca L. +1
Mathematics · #05E10 #17B10 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 17B67 #Representation Theory (math.RT) #Secondary 05A17
paper · pdf · doi:10.48550/arxiv.2208.07266
openalex publication_date 2022/08/15 · openalex created_date 2022/08/17 · openalex updated_date 2026/07/28
Consider the affine Lie algebra sℓ(n) with null root δ, weight lattice P and set of dominant weights P+. Let V(kΛ0), k ∈ ℤ≥ 1 denote the integrable highest weight sℓ(n)-module with level k ≥ 1 highest weight kΛ0. Let wt(V) denote the set of weights of V(kΛ0). A weight μ∈ wt(V) is a maximal weight if μ+ δ\not∈ wt(V). Let max+(kΛ0)= max(kΛ0)∩ P+ denote the set of maximal dominant weights which is known to be a finite set. In 2014, the authors gave the complete description of the set max+(kΛ0). In subsequent papers the multiplicities of certain subsets of max+(kΛ0) were given in terms of some pattern-avoiding permutations using the associated crystal base theory. In this paper the multiplicity of all the maximal dominant weights of the sℓ(n) -module V(kΛ0) are given generalizing the known results.