标题： 随机模型的隐藏对称性 显示英文标题

标题： Hidden Symmetries of Stochastic Models

摘要： 在矩阵乘积态方法用于$n$种类扩散过程时，稳态概率分布被表示为关于由该过程动力学确定的二次代数的矩阵乘积态。 二次代数定义了一个具有$SU_q(n)$量子群作用作为其对称性的非交换空间。 边界过程导致代数关系中出现参数依赖的线性项，并导致$SU_q(n)$对称性的降低。 我们认为不对称简单排斥过程的边界算子生成一个三对角代数，其不可约表示用 Askey-Wilson 多项式表示。 Askey-Wilson 代数作为边界问题的对称性出现，并允许精确求解该模型。 显示英文摘要

摘要： In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n)$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n)$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.