Matrix product formula for Macdonald polynomials
Matrix product formula for Macdonald polynomials
复制标题
麦克唐纳多项式的矩阵乘积公式
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Wheeler
中科院分区：
文献类型：
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作者：
L. Cantini;J. Gier;M. Wheeler
给出了对称Macdonald多项式的矩阵乘积公式。我们的结果是通过构造变形的Knizhnik-Zamolodchikov方程的多项式解得到的，该方程是通过考虑Zamolodchikov-Faddeev和Yang-Baxter代数的t-变形玻色算子的表示而产生的。这些解是多物种非对称排斥过程中粒子构型的广义概率，并且形成了n元多项式环的基，其元素由组成来索引。对于弱递增的合成(反主权)，这些基元与非对称的Macdonald多项式重合。我们的公式暗示了一种关于可解晶格模型的自然组合解释。它们还表明，当q=1时，多物种排斥过程定态的归一化可用Macdonald多项式得到。
We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik–Zamolodchikov equations, which arise by considering representations of the Zamolodchikov–Faddeev and Yang–Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1.