论文标题
Calogero模型重新审视，通勤哈密顿人，Hurwitz数字
Calogero model revisited, commuting Hamiltonians, Hurwitz numbers
论文作者
论文摘要
广义的Mironov-Morozov-Natanson（MMN）方程包括一组通勤操作员，可以将其视为量子Calogero-Sutherland问题的汉密尔顿人，并具有耦合常数的特殊值（自由费米昂）。这些哈密顿人可以被视为$ gl_n（c）$的包裹代数的中心。提出了另一个通勤系列的汉密尔顿人，由GL_N $中的任意矩阵$ a \参数化。这些哈密顿人与Hurwitz数字的关系与MMN方程相同，并产生Calogero-Surtheland模型的广义变体。
The generalized Mironov-Morozov-Natanson (MMN) equation includes a set of commuting operators, which can be considered as Hamiltonians for the quantum Calogero-Sutherland problem with a special value of the coupling constant (free fermion point). These Hamiltonians can be considered as the center of the enveloping algebra of the group $GL_N(C)$. Another commuting series of Hamiltonians is presented, parametrized by an arbitrary matrix $A\in GL_N$. These Hamiltonians are related to the Hurwitz numbers in the same way as in the case of the MMN equation and generate a generalized variant of the Calogero-Surtheland model.
