双对称麦克唐纳多项式的对称性和皮耶里规则

IF 1 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2024-04-24 DOI:10.1016/j.ejc.2024.103973

Manuel Concha, Luc Lapointe

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引用次数: 0

摘要

双对称麦克唐纳多项式可以通过非对称麦克唐纳多项式的反对称化和 t 对称化过程得到。利用双仿射赫克代数，我们证明了双对称麦克唐纳多项式的求值满足一般麦克唐纳多项式所满足的对称性。然后，我们得到了双对称麦克唐纳多项式的皮耶里规则，其中和是在某些垂直条带上。

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Symmetry and Pieri rules for the bisymmetric Macdonald polynomials

Bisymmetric Macdonald polynomials can be obtained through a process of antisymmetrization and $t$ -symmetrization of non-symmetric Macdonald polynomials. Using the double affine Hecke algebra, we show that the evaluation of the bisymmetric Macdonald polynomials satisfies a symmetry property generalizing that satisfied by the usual Macdonald polynomials. We then obtain Pieri rules for the bisymmetric Macdonald polynomials where the sums are over certain vertical strips.

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.