Matrix product and sum rule for Macdonald polynomials
Matrix product and sum rule for Macdonald polynomials
复制标题
麦克唐纳多项式的矩阵乘积和求和规则
DOI：
10.46298/dmtcs.6419
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发表时间：
2016
影响因子：
0.7
通讯作者：
M. Wheeler
中科院分区：
文献类型：
--
作者：
L. Cantini;J. Gier;M. Wheeler
国际观众
本文给出了对称Macdonald多项式Pλ的一个新的显式求和公式，并证明了它们可以写成（无限维）矩阵乘积上的迹.这些矩阵满足Zamolodchikov-Faddeev（ZF）代数.我们构造的ZF代数的解决方案，从一个降秩版本的杨巴克斯特代数。作为推论，我们发现多种群非对称排斥过程的平稳测度的归一化是一个Macdonald多项式，其中所有变量都等于1。
International audience
We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced version of the Yang–Baxter algebra. As a corollary, we find that the normalization of the stationary measure of the multi-species asymmetric exclusion process is a Macdonald polynomial with all variables set equal to one.