Stretched Newell-Littlewood coefficients
Stretched Newell-Littlewood coefficients
Newell-Littlewood coefficients nλ μ,v 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, cλ μ,v . Both sets of coefficients have stretched forms ctλ tμ,tv and ntλ tμ,tv , where tκ is the partition obtained by multiplying each part of the partition κ by the integer t. It is known that ctλ tμ,tv is a polynomial in t and here it is shown that ntλ tμ,tv is an Ehrhart quasi-polynomial in t with minimum quasi-period at most 2. The evaluation of ntλ tμ,tv is effected both by deriving its generating function and by establishing a hive model analogous to that used for the calculation of ctλ tμ,tv . These two approaches lead to a whole battery of conjectures about the nature of the quasi-polynomials ntλ tμ,tv . These include both positivity, stability and saturation conjectures that are supported by a significant amount of data from a range of examples.
Ehrhart quasi-polynomials., generating functions, hive model, multiplicities, Orthogonal and symplectic algebras, universal characters
1227-1256
King, Ronald C.
732bb66e-11e9-4e03-9a4b-ef038714efd8
King, Ronald C.
732bb66e-11e9-4e03-9a4b-ef038714efd8
King, Ronald C.
(2022)
Stretched Newell-Littlewood coefficients.
Algebraic Combinatorics, 5 (6), .
(doi:10.5802/alco.186).
Abstract
Newell-Littlewood coefficients nλ μ,v 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, cλ μ,v . Both sets of coefficients have stretched forms ctλ tμ,tv and ntλ tμ,tv , where tκ is the partition obtained by multiplying each part of the partition κ by the integer t. It is known that ctλ tμ,tv is a polynomial in t and here it is shown that ntλ tμ,tv is an Ehrhart quasi-polynomial in t with minimum quasi-period at most 2. The evaluation of ntλ tμ,tv is effected both by deriving its generating function and by establishing a hive model analogous to that used for the calculation of ctλ tμ,tv . These two approaches lead to a whole battery of conjectures about the nature of the quasi-polynomials ntλ tμ,tv . These include both positivity, stability and saturation conjectures that are supported by a significant amount of data from a range of examples.
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ALCO_2022__5_6_1227_0
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Accepted/In Press date: 17 May 2021
e-pub ahead of print date: 19 December 2022
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© The Author(s) 2022.
Keywords:
Ehrhart quasi-polynomials., generating functions, hive model, multiplicities, Orthogonal and symplectic algebras, universal characters
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Local EPrints ID: 475335
URI: http://eprints.soton.ac.uk/id/eprint/475335
PURE UUID: 46692685-99df-4e31-9b29-d61b7508c022
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Date deposited: 15 Mar 2023 17:44
Last modified: 17 Mar 2024 00:45
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