On Hamiltonians for Kerov functions
On Hamiltonians for Kerov functions
复制标题
关于 Kerov 函数的哈密顿量
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
A. Morozov
中科院分区：
文献类型：
--
作者：
A. Mironov;A. Morozov
Kerov Hamilton算子定义为一组以Kerov函数为公共本征函数的交换算子。在麦克唐纳多项式的特定情况下，众所周知的是指数型的鲁伊斯那斯哈密尔顿算子，但在提升到Kerov水平时，指数形状并不保留。直接提升是舒尔多项式的双线性展开，展开系数被因式分解并限制在单钩图中。然而，在麦克唐纳轨迹之外，系数并不庆祝这些性质，即使是集合中最简单的哈密顿量。这些系数很容易用特征值来表示：我们可以为每个任意的特征值集建立一个，这些特征值独立地为每个杨氏图R指定。这些哈密尔顿算子的一个问题是，它们是在Kostka矩阵的帮助下构造的，而不是定义它，因此比Ruijsenaars的哈密尔顿算子更弱。
Kerov Hamiltonians are defined as a set of commuting operators which have Kerov functions as common eigenfunctions. In the particular case of Macdonald polynomials, well known are the exponential Ruijsenaars Hamiltonians, but the exponential shape is not preserved in lifting to the Kerov level. Straightforwardly lifted is a bilinear expansion in Schur polynomials, the expansion coefficients being factorized and restricted to single-hook diagrams. However, beyond the Macdonald locus, the coefficients do not celebrate these properties, even for the simplest Hamiltonian in the set. The coefficients are easily expressed in terms of the eigenvalues: one can build one for each arbitrary set of eigenvalues $${E_R}$$ { E R } , specified independently for each Young diagrams R . A problem with these Hamiltonians is that they are constructed with the help of Kostka matrix instead of defining it, and thus are less powerful than the Ruijsenaars ones.
DOI：
10.48550/arxiv.1308.2177
发表时间：
2013
期刊：
--
影响因子：
--
作者：
Bytsenko A
通讯作者：
Bytsenko A