
arXiv: 2311.12216
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.
Symmetric functions and generalizations, Combinatorial aspects of representation theory, nonsymmetric Macdonald polynomials, Young diagrams, FOS: Mathematics, 05E05, Mathematics - Combinatorics, Combinatorics (math.CO), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), affine Hecke algebras
Symmetric functions and generalizations, Combinatorial aspects of representation theory, nonsymmetric Macdonald polynomials, Young diagrams, FOS: Mathematics, 05E05, Mathematics - Combinatorics, Combinatorics (math.CO), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), affine Hecke algebras
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