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no. 6
Type A partially-symmetric Macdonald polynomials
Goodberry, Ben1
1 Salisbury University Deptartment of Mathematical Sciences 1101 Camden Ave Salisbury MD 21801(USA)
Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1647-1694.

We construct type A partially-symmetric Macdonald polynomials P (λ∣γ) , where λ∈ℤ ≥0 n-k is a partition and γ∈ℤ ≥0 k is a composition. These are polynomials which are symmetric in the first n-k variables, but not necessarily in the final k variables. We establish their stability and an integral form defined using Young diagram statistics. Finally, we build Pieri-type rules for degree 1 products x j P (λ∣γ) for j>n-k and e 1 [x 1 ,⋯,x n-k ]P (λ∣γ) , along with substantial combinatorial simplification of the e 1 multiplication. The P (λ∣γ) are the same as the m-symmetric Macdonald polynomials defined by Lapointe in [9] up to a change of variables.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.388
Classification: 05E05, 05E10
Mots-clés : nonsymmetric Macdonald polynomials, affine Hecke algebras, Young diagrams

Goodberry, Ben 1

1 Salisbury University Deptartment of Mathematical Sciences 1101 Camden Ave Salisbury MD 21801(USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Goodberry, Ben. Type A partially-symmetric Macdonald polynomials. Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1647-1694. doi : 10.5802/alco.388. https://alco.centre-mersenne.org/articles/10.5802/alco.388/

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