2021/01/04 by Ronald C. King, King, Ronald C
Computer Science · Mathematics · #05E10 (Primary) #20C15 (Secondary) #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2101.00984
openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Newell-Littlewood coefficients nμ,νλ are the multiplicities occurring in the decomposition of products of universal characters of the orthogonal and symplectic groups. They may also be expressed, or even defined directly in terms of Littlewood-Richardson coefficients, cμ,νλ. Both sets of coefficients have stretched forms ctμ,tνtλ and ntμ,tνtλ, where tκ is the partition obtained by multiplying each part of the partition κ by the integer t. It is known that ctμ,tνtλ is a polynomial in t and here it is shown that ntμ,tνtλ is an Ehrhart quasi-polynomial in t with minimum quasi-period at most 2. The evaluation of ntμ,tνtλ is effected both by deriving their generating function and by establishing a hive model analogous to that used for the calculation of ctμ,tνtλ. These two approaches lead to a whole battery of conjectures about the nature of the quasi-polynomials ntμ,tνtλ. These include both positivity, stability and saturation conjectures that are supported by a significant amount of data from a range of examples.