Free field approach to the Macdonald process
Free field approach to the Macdonald process
复制标题
麦克唐纳过程的自由场方法
DOI：
10.1007/s10801-020-00976-x
复制
发表时间：
2020
影响因子：
0.8
通讯作者：
Koshida Shinji
中科院分区：
文献类型：
--
作者：
Nishizawa B;Sugawara T;Thiebot JB;Young L;Vanderwerf E;Sato F;Tomita N;Minami H;Yoda K;Watanuki Y;Koshida Shinji
Macdonald过程是划分集上的一个随机过程，它是Schur过程的(q，t)变形推广。本文讨论了用Heisenberg代数的Fock表示来识别对称函数空间的Macdonald过程。利用Macdonald对称函数对角化算符的自由场实现，提出了一种计算Macdonald过程中几个关联函数的方法。众所周知，麦克唐纳过程的几个观测值的期望值是允许行列式表示的。我们发现，这种行列式结构在相应算符的自由场实现中是明显的，而且，它在舒尔极限下的自由费米子语言中具有自然的解释。我们还根据最近对广义Macdonald函数的研究提出了广义Macdonald测度，它的存在依赖于Ding-Iohara-Miki代数的Hopf代数结构。
The Macdonald process is a stochastic process on the collection of partitions that is a (q,t)-deformed generalization of the Schur process. In this paper, we approach the Macdonald process identifying the space of symmetric functions with a Fock representation of a Heisenberg algebra. By using the free field realization of operators diagonalized by the Macdonald symmetric functions, we propose a method of computing several correlation functions with respect to the Macdonald process. It is well known that expectation value of several observables for the Macdonald process admits determinantal expression. We find that this determinantal structure is apparent in free field realization of the corresponding operators and, furthermore, it has a natural interpretation in the language of free fermions at the Schur limit. We also propose a generalized Macdonald measure motivated by recent studies on generalized Macdonald functions whose existence relies on the Hopf algebra structure of the Ding–Iohara–Miki algebra.